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We introduce the alchemical harmonic approximation (AHA) of the absolute electronic energy for charge-neutral iso-electronic diatomics at fixed interatomic distance d0. To account for variations in distance, we combine AHA with this ansatz for the electronic binding potential, E (d) = ( E u − E s ) E c − E s E u − E s d / d 0 + E s , where Eu, Ec, Es correspond to the energies of the united atom, calibration at d0, and the sum of infinitely separated atoms, respectively. Our model covers the two-dimensional electronic potential energy surface spanned by distances of 0.7–2.5 Å and differences in nuclear charge from which only one single point (with elements of nuclear charge Z1, Z2, and distance d0) is drawn to calibrate Ec. Using reference data from pbe0/cc-pVDZ, we present numerical evidence for the electronic ground-state of all neutral diatomics with 8, 10, 12, and 14 electrons. We assess the validity of our model by comparison to legacy interatomic potentials (harmonic oscillator, Lennard-Jones, and Morse) within the most relevant range of binding (0.7–2.5 Å) and find comparable accuracy if restricted to single diatomics and significantly better predictive power when extrapolating to the entire iso-electronic series. We also investigated Δ-learning of the electronic absolute energy using our model as a baseline. This baseline model results in a systematic improvement, effectively reducing training data needed for reaching chemical accuracy by up to an order of magnitude from ∼1000 to ∼100. By contrast, using AHA+Morse as a baseline hardly leads to any improvement and sometimes even deteriorates the predictive power. Inferring the energy of unseen CO converges to a prediction error of ∼0.1 Ha in direct learning and ∼0.04 Ha with our baseline. [ABSTRACT FROM AUTHOR]

We propose an estimator that allows us to calculate the value of a simple system's partition function using finite sampling. The core idea is to neglect the contribution from high energy microstates, which are difficult to be sampled properly, and then calculate a volume correction term to compensate for this. As a proof of concept, the estimator is applied to calculate the partition function for several model systems, ranging from a simple harmonic oscillator to a Lennard-Jones fluid with hundreds of particles. Our results agree well with the numerically exact solutions or reference data, demonstrating that efficiently estimating partition functions for the studied example cases is possible and computationally affordable. [ABSTRACT FROM AUTHOR]

We recently introduced the Alchemical Integral Transform (AIT), enabling the prediction of energy differences, and guessed an ansatz to parameterize space r in some alchemical change λ. Here, we present a rigorous derivation of AIT's kernel K and discuss the parameterization r(λ) in n dimensions, i.e., necessary conditions, mathematical freedoms, and additional constraints when obtaining it. Analytical expressions for changes in energy spectra and densities are given for a number of systems. Examples include homogeneous potentials such as the quantum harmonic oscillator, hydrogen-like atom, and Dirac well, both for one- and multiparticle cases, and a multiparticle system beyond coordinate scaling for harmonic potentials. [ABSTRACT FROM AUTHOR]

Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and powerful approaches to the study of electronic structure, but its application is often hindered by a steep learning curve; hence it is rarely addressed in undergraduate and postgraduate classes. This tutorial is a step toward filling this gap. We offer an introduction to the diffusion Monte Carlo (DMC) method, which aims to solve the imaginary time Schrödinger equation through stochastic sampling of the configuration space. Starting from the theoretical foundations, the discussion leads naturally to the formulation of a step-by-step algorithm. To illustrate how the method works in simplified scenarios, examples such as the harmonic oscillator and the hydrogen atom are provided. The discussion extends to the fixed-node approximation, a crucial approach for addressing the fermionic sign problem in multi-electron systems. In particular, we examine the influence of trial wave function nodal surfaces on the accuracy of DMC energy by evaluating results from a non-interacting two-fermion system. Extending the method to excited states is feasible in principle, but some additional considerations are needed, supported by practical insights. By addressing the fundamental concepts from a hands-on perspective, we hope this tutorial will serve as a valuable guide for researchers and students approaching DMC for the first time. [ABSTRACT FROM AUTHOR]

Vibrational strong coupling (VSC), the strong coupling between a Fabry–Perrot cavity and molecular vibrations at mid-infrared frequencies, has received important attention in the last years due to its capacity of modifying both vibrational spectra and chemical reactivity. VSC is a collective effect, and in this work, we introduce Path Integral Monte Carlo (PIMC) simulations that not only take into account the quantum character of the molecular vibrations and of the optical resonance of the cavity but also reproduce this collective behavior by considering multiple replicas of the molecular system. Moreover, we show that it is possible to extract from the PIMC simulations the decomposition of the hybrid optical and molecular states in terms of the bare molecular modes. On a model system of an ensemble of disordered Morse oscillators coupled to a single cavity through the Pauli–Fierz Hamiltonian, PIMC can retrieve known features obtained from analytical modes such as the Tavis–Cummings model and obtain a very close agreement with exact diagonalization for a small number of Morse oscillators. We also find that notwithstanding the anhamonic character of the Morse oscillators, the collective mode coupled to the cavity behaves as a harmonic oscillator, following the quantum central limit theorem. [ABSTRACT FROM AUTHOR]

The information engine is a feedback mechanism that extorts work from a single heat bath using the mutual information earned during the measurement. We consider an overdamped active Ornstein–Uhlenbeck particle trapped in a 1D harmonic oscillator. The particle experiences fluctuations from an inherent thermal bath with a diffusion coefficient (D) and an active reservoir, with characteristic correlation time (τa) and strength (Da). We design a feedback-driven active Brownian information engine (ABIE) and analyze its best performance criteria. The optimal functioning criteria, the information gained during measurement, and the excess output work are reliant on the dispersion of the steady-state distribution of the particle's position. The extent of enhanced performance of such ABIE depends on the relative values of two underlying time scales of the process, namely, thermal relaxation time (τr) and the characteristic correlation time (τa). In the limit of τa/τr → 0, one can achieve the upper bound on colossal work extraction as ∼ 0.202 γ (D + D a ) (γ is the friction coefficient). The excess amount of extracted work reduces and converges to its passive counterpart (∼ 0.202 γ D) in the limit of τa/τr → high. Interestingly, when τa/τr = 1, half the upper bound of excess work is achieved irrespective of the strength of either reservoirs, thermal or active. Finally, we look into the average displacement of active Brownian particles in each feedback cycle, which surpasses its thermal analog due to the broader marginal probability distribution. [ABSTRACT FROM AUTHOR]

This article introduces an advanced Koopman mode decomposition (KMD) technique—coined Featurized Koopman Mode Decomposition (FKMD)—that uses delay embedding and a learned Mahalanobis distance to enhance analysis and prediction of high-dimensional dynamical systems. The delay embedding expands the observation space to better capture underlying manifold structures, while the Mahalanobis distance adjusts observations based on the system's dynamics. This aids in featurizing KMD in cases where good features are not a priori known. We show that FKMD improves predictions for a high-dimensional linear oscillator, a high-dimensional Lorenz attractor that is partially observed, and a cell signaling problem from cancer research. [ABSTRACT FROM AUTHOR]

An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a fixed time-increment (τ > 0), it was generally believed that there exists a unique Hamiltonian producing a continuous trajectory that coincides at all discrete times (t = nτ with n integers) as long as τ is small enough. However, it is now exactly demonstrated that, for any given discrete symplectic dynamics of a harmonic oscillator, there exist an infinite number of real-valued Hamiltonians for any small value of τ and an infinite number of complex-valued Hamiltonians for any large value of τ. In addition, when the transition matrix is similar to a Jordan normal form with the supradiagonal element of 1 and the two identical diagonal elements of either 1 or −1, only one solution to the Hamiltonian is found for the case with the diagonal elements of 1, but no solution can be found for the other case. [ABSTRACT FROM AUTHOR]

In non-perturbative non-Markovian open quantum systems, reaching either low temperatures with the hierarchical equations of motion (HEOM) or high temperatures with the Thermalized Time Evolving Density Operator with Orthogonal Polynomials Algorithm (T-TEDOPA) formalism in Hilbert space remains challenging. We compare different ways of modeling the environment. Sampling the Fourier transform of the bath correlation function, also called temperature dependent spectral density, proves to be very effective. T-TEDOPA [Tamascelli et al., Phys. Rev. Lett. 123, 090402 (2019)] uses a linear chain of oscillators with positive and negative frequencies, while HEOM is based on the complex poles of an optimized rational decomposition of the temperature dependent spectral density [Xu et al., Phys. Rev. Lett. 129, 230601 (2022)]. Resorting to the poles of the temperature independent spectral density and of the Bose function separately is an alternative when the problem due to the huge number of Bose poles at low temperatures is circumvented. Two examples illustrate the effectiveness of the HEOM and T-TEDOPA approaches: a benchmark pure dephasing case and a two-bath model simulating the dynamics of excited electronic states coupled through a conical intersection. We show the efficiency of T-TEDOPA to simulate dynamics at a finite temperature by using either continuous spectral densities or only all the intramolecular oscillators of a linear vibronic model calibrated from ab initio data of a phenylene ethynylene dimer. [ABSTRACT FROM AUTHOR]

We present a general and practical theoretical framework to investigate how energy is dissipated in open quantum system dynamics. This is performed by quantifying the contributions of individual bath components to the overall dissipation of the system. The framework is based on the Nakajima–Zwanzig projection operator technique, which allows us to express the rate of energy dissipation into a specific bath degree of freedom by using traces of operator products. The approach captures system-bath interactions to all orders, but is based on second-order perturbation theory on the off-diagonal subsystem's couplings and a Markovian description of the bath. The usefulness of our theory is demonstrated by applying it to various models of open quantum systems involving harmonic oscillators or spin baths and connecting the outcomes to existing results such as our previously reported formula derived for locally coupled harmonic baths [Kim and Franco, J. Chem. Phys. 154, 084109 (2021)]. We also prove that the dissipation calculated by our theory rigorously satisfies thermodynamic principles such as energy conservation and detailed balance. Overall, the strategy can be used to develop the theory and simulation of dissipation pathways to interpret and engineer the dynamics of open quantum systems. [ABSTRACT FROM AUTHOR]

The combination of vibrational perturbation theory with the replacement of the harmonic oscillator quantization condition along the reaction coordinate with an imaginary action to be used in the uniform semiclassical approximation for the transmission probability has been shown in recent years to be a practical method for obtaining thermal reaction rates. To date, this theory has been developed systematically only up to second order in perturbation theory. Although it gives the correct leading order term in an ℏ2 expansion, its accuracy at lower temperatures, where tunneling becomes important, is not clear. In this paper, we develop the theory to fourth order in the action. This demands developing the quantum perturbation theory up to sixth order. Remarkably, we find that the fourth order theory gives the correct ℏ4 term in the expansion of the exact thermal rate. The relative magnitude of the fourth order correction as compared to the second order term objectively indicates the accuracy of the second order theory. We also extend the previous modified second order theory to the fourth order case, creating an ℏ2 modified potential for this purpose. The resulting theory is tested on the standard examples—symmetric and asymmetric Eckart potentials and a Gaussian potential. The modified fourth order theory is remarkably accurate for the asymmetric Eckart potential. [ABSTRACT FROM AUTHOR]

Environmental effects in excitation energy transfer have mostly been modeled by baths of harmonic oscillators, but to what extent such modeling provides a reliable description of actual interactions between molecular systems and environments remains an open issue. We address this issue by investigating fluctuations in the excitation energies of the light harvesting 2 complex using a realistic all-atomistic simulation of the potential energy surface. Our analyses reveal that molecular motions exhibit significant anharmonic features, even for underdamped intramolecular vibrations. In particular, we find that the anharmonicity contributes to the broadening of spectral densities and substantial overlaps between neighboring peaks, which complicates the meaning of mode frequencies constituting a bath model. Thus, we develop a strategy to construct a minimally underdamped harmonic bath that has a clear connection to all-atomistic dynamics by utilizing actual normal modes of molecules but optimizing their frequencies such that the resulting bath model can best reproduce the all-atomistic simulation results. By subtracting the underdamped contribution from the entire fluctuations, we also show that identifying a residual spectral density representing all other contributions with overdamped behavior is possible. We find that this can be fitted well with a well-established analytic form of a spectral density function or, alternatively, modeled as explicit time dependent fluctuations with muti-exponential or power law type correlation functions. We provide an assessment and the implications of these possibilities. The approach presented here can also serve as a general strategy to construct a simplified bath model that can effectively represent the underlying all-atomistic bath dynamics. [ABSTRACT FROM AUTHOR]

We ran molecular dynamics simulations of folded graphene sheets and present a procedure to measure the sliding friction in these systems based on the rate of decay of a damped harmonic oscillator. This procedure allowed us to study the effect that the size, geometry, and the temperature of the graphene sheet had on the ability to propagate the initial fold and the rate at which it settles to a final "fully folded" equilibrium state. We offer simple rationalizations for the relationships between the initial geometries of our simulations and the friction values that emerge. [ABSTRACT FROM AUTHOR]

Hydrogen clathrate hydrates are ice-like crystalline substances in which hydrogen molecules are trapped inside polyhedral cages formed by the water molecules. Small cages can host only a single H2 molecule, while each large cage can be occupied by up to four H2 molecules. Here, we present a neutron scattering study on the structure of the sII hydrogen clathrate hydrate and on the low-temperature dynamics of the hydrogen molecules trapped in its large cages, as a function of the gas content in the samples. We observe spectral features at low energy transfer (between 1 and 3 meV), and we show that they can be successfully assigned to the rattling motion of a single hydrogen molecule occupying a large water cage. These inelastic bands remarkably lose their intensity with increasing the hydrogen filling, consistently with the fact that the probability of single occupation (as opposed to multiple occupation) increases as the hydrogen content in the sample gets lower. The spectral intensity of the H2 rattling bands is studied as a function of the momentum transfer for partially emptied samples and compared with three distinct quantum models for a single H2 molecule in a large cage: (i) the exact solution of the Schrödinger equation for a well-assessed semiempirical force field, (ii) a particle trapped in a rigid sphere, and (iii) an isotropic three-dimensional harmonic oscillator. The first model provides good agreement between calculations and experimental data, while the last two only reproduce their qualitative trend. Finally, the radial wavefunctions of the three aforementioned models, as well as their potential surfaces, are presented and discussed. [ABSTRACT FROM AUTHOR]

When used as pump pulses in transient absorption spectroscopy measurements, femtosecond laser pulses can produce oscillatory signals known as quantum beats. The quantum beats arise from coherent superpositions of the states of the sample and are best studied in the Fourier domain using Femtosecond Coherence Spectroscopy (FCS), which consists of one-dimensional amplitude and phase plots of a specified oscillation frequency as a function of the detection frequency. Prior works have shown ubiquitous amplitude nodes and π phase shifts in FCS from excited-state vibrational wavepackets in monomer samples. However, the FCS arising from vibronic-exciton states in molecular aggregates have not been studied theoretically. Here, we use a model of vibronic-exciton states in molecular dimers based on displaced harmonic oscillators to simulate FCS for dimers in two important cases. Simulations reveal distinct spectral signatures of excited-state vibronic-exciton coherences in molecular dimers that may be used to distinguish them from monomer vibrational coherences. A salient result is that, for certain relative orientations of the transition dipoles, the key resonance condition between the electronic coupling and the frequency of the vibrational mode may yield strong enhancement of the quantum-beat amplitude and, perhaps, also cause a significant decrease of the oscillation frequency to a value far lower than the vibrational frequency. Future studies using these results will lead to new insights into the excited-state coherences generated in photosynthetic pigment–protein complexes. [ABSTRACT FROM AUTHOR]

In this article, we show that the collective light–matter strong coupling regime where N molecular emitters couple to the photon mode of an optical cavity can be mapped to a quantum impurity model where the photon is the impurity that is coupled to a bath of anharmonic transitions. In the thermodynamic limit where N ≫ 1, we argue that the bath can be replaced with an effective harmonic bath, leading to a dramatic simplification of the problem into one of the coupled harmonic oscillators. We derive simple analytical expressions for linear optical spectra (transmission, reflection, and absorption) where the only molecular input required is the molecular linear susceptibility. This formalism is applied to a series of illustrative examples, showing the role of temperature, disorder, vibronic coupling, and optical saturation of the molecular ensemble, explaining that it is useful even when describing an important class of nonlinear optical experiments. For completeness, we provide Appendixes A–C that include a self-contained derivation of the relevant spectroscopic observables for arbitrary anharmonic systems (for both large and small N) within the rotating-wave approximation. While some of the presented results herein have already been reported in the literature, we provide a unified presentation of the results as well as new interpretations that connect powerful concepts in open quantum systems and linear response theory with molecular polaritonics. [ABSTRACT FROM AUTHOR]

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller–Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree–Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm−1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm−1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two ab initio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems. [ABSTRACT FROM AUTHOR]

Tracer diffusion in polymer networks and hydrogels is relevant in biology and technology, while it also constitutes an interesting model process for the dynamics of molecules in fluctuating, heterogeneous soft matter. Here, we systematically study the time-dependent dynamics and (non-Markovian) memory effects of tracers in polymer networks based on (Markovian) implicit-solvent Langevin simulations. In particular, we consider spherical tracer solutes at high dilution in regular, tetrafunctional bead-spring polymer networks and control the tracer–network Lennard-Jones (LJ) interactions and the polymer density. Based on the analysis of the memory (friction) kernels, we recover the expected long-time transport coefficients and demonstrate how the short-time tracer dynamics, polymer fluctuations, and the viscoelastic response are interlinked. Furthermore, we fit the characteristic memory modes of the tracers with damped harmonic oscillations and identify LJ contributions, bond vibrations, and slow network relaxations. Tuned by the LJ interaction parameter, these modes enter the kernel with an approximately linear to quadratic scaling, which we incorporate into a reduced functional form for convenient tracer memory interpolation and extrapolation. This eventually leads to highly efficient simulations utilizing the generalized Langevin equation, in which the polymer network acts as an additional thermal bath with a tunable intensity. [ABSTRACT FROM AUTHOR]

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker–Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole–dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé–Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory. [ABSTRACT FROM AUTHOR]

By using the recently derived universal discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically and evaluated numerically at each imaginary time step for any short-time propagator. This work shows that, using only currently known short-time propagators, the Hamiltonian energy can be optimized to the twelfth-order, converging to the ground state energy of the harmonic oscillator in as few as three beads. This study makes it absolutely clear that the widely used second-order primitive approximation propagator, when used in computing thermodynamic energy, converges extremely slowly with an increasing number of beads. [ABSTRACT FROM AUTHOR]

It has been assumed that the negative divergence of all stress tensors in common use yields the same force. This work finds that this is untrue, and, in fact, can vary wildly. We demonstrate this for the hydrogen atom, the one-particle isotropic harmonic oscillator, and a particle in an infinite spherical well where the exact density, pair-density, and the first order reduced density matrix are known for ground and excited states without any approximation. The Ehrenfest stress-tensor is introduced as any stress-tensor whose negative divergence will yield the corresponding Ehrenfest force for the same system when the exact wave-function is utilized. Stress-tensors within the literature are examined to show those that are Ehrenfest stress-tensors. Those that differ are demonstrated by how they differ within an exact formulation. The proof that the negative divergence of an Ehrenfest stress-tensor yields the Ehrenfest force is summarized. [ABSTRACT FROM AUTHOR]

The time-dependent rotational and vibrational temperatures were measured to study the shock-heated thermal nonequilibrium behaviors of CO with Ar, He, and H2 as collision partners. Three interference-free transition lines in the fundamental vibrational band of CO were applied to the fast, in situ, and state-specific measurements. Vibrational relaxation times of CO were summarized over a temperature range of 1110–2820 K behind reflected shocks. The measured rotational temperature instantaneously reached an equilibrium state behind shock waves. The measured vibrational temperature experienced a relaxation process before reaching the equilibrium state. The measured vibrational temperature time histories were compared with predictions based on the Landau–Teller model and the state-to-state approach. The state-to-state approach treats the vibrational energy levels of CO as pseudo-species and accurately describes the detailed thermal nonequilibrium processes behind shock waves. The datasets of state-specific inelastic rate coefficients of CO–Ar, CO–He, CO–CO, and CO–H2 collisions were calculated in this study using the mixed quantum-classical method and the semiclassical forced harmonic oscillator model. The predictions based on the state-to-state approach agreed well with the measured data and nonequilibrium (non-Boltzmann) vibrational distributions were found in the post-shock regions, while the Landau–Teller model predicted slower vibrational temperature time histories than the measured data. Modifications were applied to the Millikan–White vibrational relaxation data of the CO–Ar and CO–H2 systems to improve the performance of the Landau–Teller model. In addition, the thermal nonequilibrium processes behind incident shocks, the acceleration effects of H2O on the relaxation process of CO, and the characterization of vibrational temperature were highlighted. [ABSTRACT FROM AUTHOR]

The performance of Hamiltonian Monte Carlo simulations crucially depends on both the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters based on a local loss function that promotes the fast exploration of phase space. We show that a good correspondence between loss and autocorrelation time can be established, allowing for gradient-based optimization using a fully differentiable set-up. The loss is constructed in such a way that it also allows for gradient-driven learning of a distribution over the number of integration steps. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein commonly used as a test case for simulation methods. Through the application to the harmonic oscillator, we highlight the importance of not using a fixed timestep to avoid a rugged loss surface with many local minima, otherwise trapping the optimization. In the case of alanine dipeptide, by tuning the only free parameter of our loss definition, we find a good correspondence between it and the autocorrelation times, resulting in a > 100 fold speedup in the optimization of simulation parameters compared to a grid search. For this system, we also extend the integrator to allow for atom-dependent timesteps, providing a further reduction of 25% in autocorrelation times. [ABSTRACT FROM AUTHOR]

The time-dependent rotational and vibrational temperatures were measured to study the shock-heated thermal nonequilibrium behaviors of CO with Ar, He, and H2 as collision partners. Three interference-free transition lines in the fundamental vibrational band of CO were applied to the fast, in situ, and state-specific measurements. Vibrational relaxation times of CO were summarized over a temperature range of 1110–2820 K behind reflected shocks. The measured rotational temperature instantaneously reached an equilibrium state behind shock waves. The measured vibrational temperature experienced a relaxation process before reaching the equilibrium state. The measured vibrational temperature time histories were compared with predictions based on the Landau–Teller model and the state-to-state approach. The state-to-state approach treats the vibrational energy levels of CO as pseudo-species and accurately describes the detailed thermal nonequilibrium processes behind shock waves. The datasets of state-specific inelastic rate coefficients of CO–Ar, CO–He, CO–CO, and CO–H2 collisions were calculated in this study using the mixed quantum-classical method and the semiclassical forced harmonic oscillator model. The predictions based on the state-to-state approach agreed well with the measured data and nonequilibrium (non-Boltzmann) vibrational distributions were found in the post-shock regions, while the Landau–Teller model predicted slower vibrational temperature time histories than the measured data. Modifications were applied to the Millikan–White vibrational relaxation data of the CO–Ar and CO–H2 systems to improve the performance of the Landau–Teller model. In addition, the thermal nonequilibrium processes behind incident shocks, the acceleration effects of H2O on the relaxation process of CO, and the characterization of vibrational temperature were highlighted. [ABSTRACT FROM AUTHOR]

We study entanglement in a simple model comprising two coupled linear harmonic oscillators of the same natural frequency. The system is separable in the center of mass (COM) and relative coordinates into two oscillators of frequency ωc and ωr. We compute standard entanglement measures (subsystem linear entropy and subsystem von Neumann entropy) as well as several tomographic entanglement indicators (Bhattacharyya distance, Kullback–Leibler divergence, and inverse participation ratio) as functions of the frequency ratio η = ωc/ωr, keeping the COM oscillator in its ground state. We demonstrate that, overall, the entanglement indicators reflect quite faithfully the variations in the standard measures. The entanglement is shown to be minimum at η = 1 and maximum at η → 0 or ∞. [ABSTRACT FROM AUTHOR]

We prove boundedness results on modulation and Wiener amalgam spaces for some families of spectral multipliers for the twisted Laplacian. We exploit the metaplectic equivalence relating the twisted Laplacian with a partial harmonic oscillator, leading to a general transference principle for the corresponding spectral multipliers. Our analysis encompasses powers of the twisted Laplacian and oscillating multipliers, with applications to the corresponding Schrödinger and wave flows. On the other hand, elaborating on the twisted convolution structure of the eigenprojections and its connection with the Weyl product of symbols, we obtain a complete picture of the boundedness of the heat flow for the twisted Laplacian. Results of the same kind are established for fractional heat flows via subordination. [ABSTRACT FROM AUTHOR]

In this paper, the Feynman path integral approach within three parameters Dunkl derivative is investigated in the one-dimensional case of nonrelativistic quantum mechanics. We successfully derive the propagator in Cartesian coordinates and give its exact expression for the free particle, inverse square, harmonic oscillator and pure Coulomb potentials. The energy eigenvalues and their corresponding wave functions are determined. [ABSTRACT FROM AUTHOR]

The dynamics of neuronal systems are characterized by hallmark features such as oscillations and synchrony. However, it has remained unclear whether these characteristics are epiphenomena or are exploited for computation. Due to the challenge of selectively interfering with oscillatory network dynamics in neuronal systems, we simulated recurrent networks of damped harmonic oscillators in which oscillatory activity is enforced in each node, a choice well supported by experimental findings. When trained on standard pattern recognition tasks, these harmonic oscillator recurrent networks (HORNs) outperformed nonoscillatory architectures with respect to learning speed, noise tolerance, and parameter efficiency. HORNs also reproduced a many characteristic features of neuronal systems, such as the cerebral cortex and the hippocampus. In trained HORNs, stimulus-induced interference patterns holistically represent the result of comparing sensory evidence with priors stored in recurrent connection weights, and learning-induced weight changes are compatible with Hebbian principles. Implementing additional features characteristic of natural networks, such as heterogeneous oscillation frequencies, inhomogeneous conduction delays, and network modularity, further enhanced HORN performance without requiring additional parameters. Taken together, our model allows us to give plausible a posteriori explanations for features of natural networks whose computational role has remained elusive. We conclude that neuronal systems are likely to exploit the unique dynamics of recurrent oscillator networks whose computational superiority critically depends on the oscillatory patterning of their nodal dynamics. Implementing the proposed computational principles in analog hardware is expected to enable the design of highly energy-efficient and self-adapting devices that could ideally complement existing digital technologies. [ABSTRACT FROM AUTHOR]

In this paper, we determine the radial and orbital states mass spectra of the triply heavy baryon Ωbbc with total spin S=1∕2 and 3/2 using the hypercentral constituent quark model (hCOM). The mass spectra are obtained by incorporating the color Coulomb plus linear confining term and the harmonic oscillator potential with first-order correction. Additionally, we considered spin–spin, spin-orbit and tensor interactions for hyperfine splitting calculation. Our computed mass spectra of the Ωbbc baryon is compared with existing literature. Further, we establish Regge trajectories of this baryon in (n,M2) and (J,M2) planes which are helpful in determining the unknown quantum number and JP values. [ABSTRACT FROM AUTHOR]

We propose and analyze a universal method to obtain fast charging of a quantum battery by a driven charger system using controlled, pure dephasing of the charger. While the battery displays coherent underdamped oscillations of energy for weak charger dephasing, the quantum Zeno freezing of the charger energy at high dephasing suppresses the rate of transfer of energy to the battery. Choosing an optimum dephasing rate between the regimes leads to a fast charging of the battery. We illustrate our results with the charger and battery modeled by either two-level systems or harmonic oscillators. Apart from the fast charging, the dephasing also renders the charging performance more robust to detuning between the charger, drive, and battery frequencies for the two-level systems case. [ABSTRACT FROM AUTHOR]

Quantum control of a linear oscillator using a static dispersive coupling to a nonlinear ancilla underpins a wide variety of experiments in circuit QED. Extending this control to more than one oscillator while minimizing the required connectivity to the ancilla would enable hardware-efficient multi-mode entanglement and measurements. We show that the spectrum of an ancilla statically coupled to a single mode can be made to depend on the joint photon number in two modes by applying a strong parametric beamsplitter coupling between them. This 'joint-photon number-splitting' regime extends single-oscillator techniques to two-oscillator control, which we use to realize a hardware-efficient erasure check for a dual-rail qubit encoded in two superconducting cavities. This scheme leverages the high-fidelity beamsplitter coupling already required for single- and two-qubit gates while permitting minimal crosstalk between circuit elements. Furthermore, the flexibility to choose the pulse shape allows us to limit the susceptibility to different error channels. We use this scheme to detect leakage errors with a missed erasure fraction of (9.0 ± 0.5) × 10−4 while incurring an erasure rate of 2.92 ± 0.01% and a Pauli error rate of 0.31 ± 0.01%, both of which are dominated by cavity errors. [ABSTRACT FROM AUTHOR]

In this article, we investigate the edge localized mode (ELM)-free quiescent H (QH)-mode regime in the HL-3 tokamak via nonlinear MHD simulations. HL-3 (previously known as HL-2M) aims at high β plasmas and recently achieved its first H-mode operation. Large ELMs in H-mode discharges challenge the tolerance of plasma facing components in reactor-relevant tokamaks and small/no-ELM regimes become attractive options for existing and future fusion devices. A naturally ELM-free regime, QH-mode, is explored in this work with nonlinear extended MHD modeling for the HL-3 device. The simulation is conducted based on a realistic lower single null divertor configuration, and successfully produces a QH-mode plasma. Toroidal modes n = 0 , ... , 12 are simulated and the QH-mode plasma is dominated by a saturated n = 2 kink-peeling mode. After entering QH-mode, the plasma thermal energy becomes nearly stationary and the plasma pedestal is kept at a stable level. The saturated peeling instability produces an ergodized edge magnetic field region and some E × B convective cells, which enhance radial transport. The edge harmonic oscillation (EHO) as a characteristic feature of QH-mode plasmas is detected in the pedestal with a fundamental frequency (for the n = 1 mode) of 7.5 kHz. The EHO structures on the high-field side (HFS) and low-field side (LFS) are observed to be asymmetric. The EHO is dominated by the n = 2 mode with a frequency of 15 kHz on the HFS, while the n = 3 mode becomes dominant at the vicinity of ψ norm = 0.95 on the LFS. It is also found that density and temperature profiles show different responses to the EHO in the simulation. The dependence on the safety factor for accessing QH-mode is demonstrated with the QH-mode being lost when q95 is reduced from 2.5 to 2.3. The EHO is absent in this scenario and a bursting ELM-like activity is observed instead. [ABSTRACT FROM AUTHOR]

Starting from a Wheeler–DeWitt type equation for an uncharged black hole Q = 0 , and by choosing the order parameter (s = 2) and running the gravitational degrees of freedom it is possible to reduce the Wheeler–DeWitt equation to the canonical form of a quantum harmonic oscillator. In this direction, a natural frequency of oscillation is identified for the black hole. The entanglement entropy of a pair of interacting quantum black holes of mass M is obtained and analyzed. Here we consider as a starting model a pair of identical oscillators of frequency ω coupled by a quadratic potential and with interaction constant given by ω c . Given the relation between the oscillation frequency ω of an isolated quantum black hole and its mass, the entanglement entropy of this system is obtained by analogy with a pair of quantum oscillators coupled by a quadratic interaction potential of frequency ω c . The analysis of the entanglement entropy is performed by introducing the reduced variables ω ~ and A ~ . An interesting result arises when we consider A ~ ≫ 1 and the interaction parameter is set ω ~ = 1 . In this case, the entanglement entropy can be replaced by its asymptotic expansion, where the dominant term is of logarithmic character in the reduced area. Another case of analysis emerges when the reduced area A ~ = 1 and ω ~ varies. In this case, the entanglement entropy depends uniquely on the interaction parameter between the two black holes. [ABSTRACT FROM AUTHOR]

We report the results of calculations of the linear polarizability and second hyperpolarizability of the H2 molecule in the bond dissociation process. These calculations were performed for isolated molecules, as well as molecules under spatial confinement. The spatial confinement was modeled using the external two-dimensional (cylindrical) harmonic oscillator potential. In contrast to the recently investigated polar LiH molecule, it was shown that the spatial confinement significantly diminishes the linear and nonlinear response of H2 for each interatomic (H-H) distance. [ABSTRACT FROM AUTHOR]

In this paper, we present a "non-linear" factorization of a family of non-normal operators arising from Gribov's theory of the following form: H λ ′ , μ , λ = λ ′ A * 2 A 2 + μ A * A + i λ A * (A + A *) A , where the quartic Pomeron coupling λ ′ , the Pomeron intercept μ and the triple Pomeron coupling λ are real parameters, and i 2 = − 1 . A * and A are, respectively, the usual creation and annihilation operators of the one-dimensional harmonic oscillator obeying the canonical commutation relation [ A , A * ] = I . In Bargmann representation, we have A ⟷ d d z and A * ⟷ z , z = x + i y . It follows that H λ ′ , μ , λ can be written in the following form: H λ ′ , μ , λ = p (z) d 2 d z 2 + q (z) d d z , where p (z) = λ ′ z 2 + i λ z and q (z) = i λ z 2 + μ z. This operator is an operator of the Heun type where the Heun operator is defined by H = p (z) d 2 d z 2 + q (z) d d z + v (z) , where p (z) is a cubic complex polynomial, q (z) and v (z) are polynomials of degree at most 2 and 1, respectively, which are given. For z = − i y , H λ ′ , μ , λ takes the following form: H λ ′ , μ , λ = − a (y) d 2 d y 2 + b (y) d d z , with a (y) = y (λ − λ ′ y) and b (y) = y (λ y + μ). We introduce the change of variable y = λ 2 λ ′ (1 − c o s (θ)) , θ ∈ [ 0 , π ] to obtain the main result of transforming H λ ′ , μ , λ into a product of two first-order operators: H ˜ λ ′ , μ , λ = λ ′ (d d θ + α (θ)) (− d d θ + α (θ)) , with α (θ) being explicitly determined. [ABSTRACT FROM AUTHOR]

We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater. [ABSTRACT FROM AUTHOR]

In 1925, Heisenberg, Born, and Jordan developed matrix mechanics as a strategy to solve quantum-mechanical problems. While finite-sized matrix formulations are commonly taught in quantum instruction, following the logic and detailed steps of the original matrix mechanics has become a lost art. In preparation for the 100th anniversary of the discovery of quantum mechanics, we present a modernized discussion of how matrix mechanics is formulated, how it is used to solve quantum-mechanical problems, and how it can be employed as the starting point for a postulate-based formulation of quantum-mechanics instruction. We focus on the harmonic oscillator to describe how quantum mechanics advanced from the Bohr–Sommerfeld quantization condition, to matrix mechanics, to the current abstract ladder-operator approach. We also describe a number of different activities that can be included in the quantum mechanics classroom to celebrate this centennial. Editor's Note: The finite spacetime manifold in which outgoing waves reach infinity in a finite spacetime interval was introduced in the 1960s by Roger Penrose. It plays an important role in the analysis of gravitational waves. In this work the author shows how to construct a temporal foliation using spacelike slices with hyperbolic geometry in compactified Minkowski space. Instructors in special relativity will be able to make these ideas accessible to their students, including an application to massless fields in flat spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we provide a glimpse of the original formulation of quantum mechanics (a.k.a. matrix mechanics), as proposed by Heisenberg, Born, and Jordan in 1925, by showing how it solves the quantum harmonic oscillator. This presentation can shed light on the relationship between different formulations and give students a deeper understanding of quantum mechanics. Editor's Note: Introductory quantum mechanics courses typically discuss only the early history of the quantum era, including the experiments that differed from classical predictions, such as black body radiation spectra, and the rough heuristic rules invented to describe these unexpected results, such as the Rydberg formula for atomic emission spectra and Bohr's correspondence principle. This "old quantum theory" built the conceptual foundations that then enabled the development of several complete mathematical formalisms, with matrix mechanics first emerging in 1925, and wave mechanics in 1926. Introductory courses typically skip this history and present only the modern formalism. Here, the arguments of Heisenberg's "magical" 1925 paper that quickly inspired Born and Jordan's matrix mechanics are used to find the energy spectrum of the quantum harmonic oscillator in a presentation appropriate for upper-level undergraduates. [ABSTRACT FROM AUTHOR]

This work deals with the key constituent behind the existence of superfluid states in ultracold fermionic gases confined in a harmonic trap in 2D, namely, the formation of Cooper pairs in the presence of a Fermi sea in inhomogeneous confinement. For a set of finite-range models representing particle–particle interaction, we first ascertain the simultaneity of the emergence of bound states and the divergence of the s-wave scattering length in 2D as a function of the interaction potential parameters in free space. Then, through the analysis of two particles interacting in 2D harmonic confinement, we evaluate the energy shift with respect to the discrete harmonic oscillator levels for both repulsive and attractive cases. All of these results are the basis for determining the energy gaps of Cooper pairs arising from two particles interacting in the presence of a Fermi sea consisting of particles immersed in a 2D harmonic trap. [ABSTRACT FROM AUTHOR]

The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all observables in one model, and the observables of the other model. Thus the duality we find, appears to be in conflict with the usual assertion that classical theories can never reproduce quantum effects as observed in many quantum models. We suggest that there must be more of such relationships, but we study only this one as a prototype. It reveals how classical hidden variables may work. The classical states can form the basis of Hilbert space that can be adopted in describing the quantum model. Wave functions in the quantum system generate probability distributions in the classical one. One finds that, where the classical system always obeys the rule probability in = probability out, the same probabilities are quantum probabilities in the quantum system. It is shown how the quantum x and p operators in a quantum oscillator can be given a classical meaning. It is explained how an apparent clash with quantum logic can be rationalized. [ABSTRACT FROM AUTHOR]

In this work, the conformable Bateman Lagrangian for the damped harmonic oscillator system is proposed using the conformable derivative concept. In other words, the integer derivatives are replaced by conformable derivatives of order α with 0 < α ≤ 1. The corresponding conformable Euler–Lagrange equations of motion and fractional Hamiltonian are then obtained. The system is then canonically quantized and the conformable Schrödinger equation is constructed. The fractional-order dependence of the energy eigenvalues E n α and eigenfunctions ψ n α is obtained using suitable transformations and the extended fractional Nikiforov–Uvarov method. The corresponding conformable continuity equation is also derived and the probability density and probability current are thus suitably defined. The probability density evolution as well as its dependence on α is plotted and analyzed for various situations. It is found that the energy eigenvalues are real and there are sort of gradual ordering in the behavior of the probability densities. [ABSTRACT FROM AUTHOR]

Collective phenomena arise from interactions within complex systems, leading to behaviors absent in individual components. Observing quantum collective phenomena with macroscopic mechanical oscillators has been impeded by the stringent requirement that oscillators be identical. We demonstrate the quantum regime for collective motion of N = 6 mechanical oscillators, a hexamer, in a super-conducting circuit optomechanical platform. By increasing the optomechanical couplings, the system transitions from individual to collective motion, characterized by a √N enhancement of cavity-collective mode coupling, akin to super-radiance of atomic ensembles. Using sideband cooling, we prepare the collective mode in the quantum ground state and measure its quantum sideband asymmetry, with zero-point motion distributed across distant oscillators. This regime of opto-mechanics opens avenues for studying multipartite entanglement, with potential advances in quantum metrology. [ABSTRACT FROM AUTHOR]

This study proposes a quantum approach to measure the tail risk of crude oil futures. Based on the quantum harmonic oscillator (QHO) model, we first model the log return process of crude oil futures. From the equilibrium distribution of QHO model, we calculate the well-known tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES); we confirm that this quantum approach provides precise estimates of in-sample and out-of-sample VaR and ES for crude oil futures. The findings suggest the QHO model for log return process outperforms the geometric Brownian motion for price process and the historical simulation approach. The excellence of QHO model in explaining the tail risk of crude oil futures can be attributed to its fast angular frequency and high probability allocation in excited states. Crude oil market participants can use this study's analytical framework to precisely measure and manage potential risks in the marketplace. Regulatory authorities can evaluate the degree of crude oil market instability through the current market state of crude oil futures characterized by the QHO model parameters while devising and revising crude oil market regulations. Future research can examine quantum models with (1) different assumptions, e.g., position-dependent diffusion and time-varying equilibrium return, and (2) different potential functions, e.g., infinite and finite square well. [ABSTRACT FROM AUTHOR]

An impact of an electronic structure or force field method, gas‐phase thermodynamic correction, and continuum solvation model on organic carbonate clusters (S)n conformational and binding energies is explored. None of the tested force field (GFN‐FF, GAFF, MMFF94) and standard semiempirical methods (PM3, AM1, RM1, PM6, PM6‐D3, PM6‐D3H4, PM7) can reproduce reference RI‐SCS‐MP2 conformational energies. Tight‐binding GFNn‐xTB methods provide more realistic conformational energies which are accurate enough to discard the least stable conformers. The effect of thermodynamic correction is moderate and can be ignored if the gas phase conformational stability ranking is a goal. The influence of continuum solvation is stronger, especially if reinforced with the Gibbs free energy thermodynamic correction, and results in the reduced spread of conformational energies. The cluster formation binding energies strongly depend on a particular approach to vibrational thermochemistry with the difference between traditional harmonic and modified scaled rigid – harmonic oscillator approximations reaching 10 kcal mol−1. [ABSTRACT FROM AUTHOR]

The molecular characteristics and rheological properties of three UHMWPE samples were investigated. The high-temperature GPC method was used for characterizing UHMWPE samples used. The interpretation of the measurement results was based on calibration using the PS standard and the approximation of the PS data by linear and cubic polynomials, as well as on the data for linear PE. The assessment of the average MW and MWD depends on the choice of calibration method, so that different methods give different results. Only the results obtained using PS with cubic approximation are close to the characteristics offered by the manufacturer. It was also shown that the obtained MW characteristics depend on the dissolution time. The reason for this may be the presence of any processing-aid compounds or destruction of macromolecules. Measurements of the rheological properties were performed in creep modes for a wide range of shear stresses and harmonic oscillations. It was shown that even at 210 °C, UHMWPE does not flow, and the observed irreversible deformations are due to the plasticity of the polymer, i.e., UHMWPE is in an elastic–plastic state. The ultimate plastic deformations drop sharply with increasing MW of the polymer. The plasticity modulus for the highest molecular weight UHMWPE samples does not depend on stress. Measurements of viscoelastic characteristics confirmed that the terminal region of viscous flow cannot be reached under any conditions. Increasing the duration of holding the polymer at high temperature leads not to flow, but to the destruction of macromolecules. [ABSTRACT FROM AUTHOR]

Macrocycles that encapsulate two guests can self-sort those into homo- and heterodimers. We report here a family of self-sorting homobimetallic Pt(II) terpyridyl acetylide dimers secured together with a pair of Cucurbit[8]uril macrocycles (CB[8]). The rigid bridging unit between both Pt centers introduces varying "hinge" angles, resulting in disparities in Pt–Pt distances in the heterodimers, and leads to recognition motif mismatch. We found that the self-sorting process can be quantified using a simple model, in which each complex behaves as a simple harmonic oscillator, whose heteroassembly tends to minimize geometry distorsions through C(aryl)–C≡C–Pt axis deformation. [ABSTRACT FROM AUTHOR]

We determine the closed-form solution of a three-dimensional stationary Schrödinger equation for an angular-dependent potential in spherical coordinates within the Dunkl formalism. Furthermore, we calculate the change of the system's total energy with respect to coupling constants in the potential by means of the Hellman–Feynman theorem. [ABSTRACT FROM AUTHOR]

This work contributes to an overview of the structure of tautomers and rotamers of 2- and 8-hydroxy azaazulene and their mercapto analogues. This can be accomplished by optimizing the structures at the B3LYP functional with the 6-311+G(d,p) basis sets. Single-point energy calculations were performed at the M06-2X/6-311++G(2d,2p) level. The G3MP2 composite method was employed to obtain more accurate energies. The variations in the local aromaticity of aromatic rings were discussed by using the nucleus-independent chemical shift (NICS), the harmonic oscillator model of aromaticity index (HOMA), the multicenter index (MCI), and the aromatic fluctuation index (FLU and FLU-π) as probes of aromaticity. Additionally, the intramolecular proton transfer and rotation barriers of tautomerization and rotamerization have been extensively discussed. The discussion also encompassed natural bond orbital (NBO) charges and analysis, as well as atoms in molecules (AIM) analysis. The results reveal the presence of intramolecular hydrogen bonds in the 8OH-AZ, 8S-AZ, and 8SH-AZ structures. [ABSTRACT FROM AUTHOR]

The dynamic behaviour of the system in power system networks is nonlinear. Due to heavy load and technical advancement, it faces several difficulties. One of the most significant factors that have a detrimental effect on the electrical network is instability in the voltage. By preserving the system voltage and removing voltage fluctuations, this work proposes the fuzzy Mamdani controller and increases voltage stability. The suggested fuzzy controller takes the place of the current PI regulator and allows for improved voltage regulation and disturbance compensation utilizing TSO (Tuna Swarm Optimization). The team-based foraging behaviour of tuna swarms served as the primary source of motivation for TSO. The work uses two tuna swarm foraging strategies—spiral foraging and parabolic foraging—as models to create an efficient metaheuristic algorithm. TSO's performance is assessed concerning many actual technical problems. As a result, non-linear power quality issues are resolved by applying the static Var compensator (SVC)-based fuzzy Mamdani approach with the TSO algorithm. The IEEE-39 bus system is used to analyse and assess the recommended approach, and it is compared to previous research. The decrease of the error in the stable state of voltage at the buses and the highest possible voltage loss that takes place following the development of a defect established the effectiveness of the proposed approach for minimizing oscillations in voltage and harmonic flows. Simulations show how well the reactive power replacement and voltage regulation work using the fuzzy Mamdani controllers that have been built in MATLAB/SIMULINK. [ABSTRACT FROM AUTHOR]

We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained corresponds to a deformed Grassmann-type algebra, involving anticommuting Grassmann-type variables. The role played by the latter in implementing gauge invariance in second quantization within our procedure is then discussed. This discussion includes the application of the mapping to the case of the bosonic and fermionic harmonic oscillator Hamiltonians. [ABSTRACT FROM AUTHOR]