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The dynamic response of dielectric elastomers is widely used in many functional devices, but current research has neglected the effect of varying dielectric permittivity on their dynamic oscillations and stability. This paper studies the thin-walled dielectric balloon in which the stretch-dependent dielectric permittivity is considered. We obtain the dynamic equation of motion by Hamilton's principle. Based on the principle of no energy dissipation in conservative systems, we establish energy conservation at the maximum stretching position and at the initial moment, then we investigate the stability in the dynamic case. It is found that a stretch-related dielectric permittivity can increase the critical electric field of the balloon and can also change the mode of electric field instability and modulate the critical stretch value. In the dynamic case, the stretch-dependent permittivity increases the critical electric field by 4 % when the balloon is only subjected to electric force; moreover, it increases the critical stretch value by 316.68 % by changing the unstable mode from pull-in instability to snap-through instability. It is hoped that this work will provide new thinking in designing functional devices by using the dynamical response and stability of dielectric elastomers. [ABSTRACT FROM AUTHOR]

The given text discusses different approaches to finding equations of motion for physical systems, such as the Newtonian, Lagrangian, and Hamiltonian approaches. It presents a supplementary tool using the total differential of the mechanical energy function to obtain equations of motion for certain systems. The text also explores the relationship between this approach and Hamilton's equations of motion. Additionally, the text provides concise and factual information about different types of motion and their corresponding equations, making it a useful resource for library patrons conducting research on these topics. [Extracted from the article]

The variational problem, Noether symmetry and conserved quantity, and Lie symmetry and conserved quantity of singular systems are investigated on the basis of Riesz derivatives. First, based on Riesz derivatives, the variational problem of Lagrangian systems is studied, the fractional Lagrange equation is established, and the primary constraint problem of the system is discussed when the Lagrangian is singular. Second, the constrained Hamilton equation is established and the compatibility condition is provided. Third, the Noether symmetry and conserved quantity and the Lie symmetry and conserved quantity of the constrained Hamiltonian system are studied. In the end, an example is provided for illustration. [ABSTRACT FROM AUTHOR]

Hybrid methods that combine molecular dynamics methods capable of analyzing dynamics with Monte Carlo (MC) methods that can efficiently treat thermodynamically stable states are valuable for understanding complex chemical processes in which an equilibrium state is reached through many elementary processes. The hybrid MC (HMC) method is one such promising method; however, it often fails to sample configurations properly from the canonical multimodal distribution due to the rugged potential energy surfaces. In this paper, we extend the HMC method to overcome this difficulty. The new method, which is termed potential scaling HMC (PS-HMC), makes use of an artificially modulated trajectory to propose a new configuration. The trajectory is generated from Hamilton's equations, but the potential energy surface is scaled to be gradually flattened and then recovered to the original surface, which facilitates barrier-crossing processes. We apply the PS-HMC method to three kinds of molecular processes: the thermal motion of argon particles, butane isomerization, and an atom transfer chemical reaction. These applications demonstrate that the PS-HMC method is capable of correctly constructing the canonical ensemble with a multimodal distribution. The sampling efficiency and accepted trajectories are examined to clarify the features of the PS-HMC method. Despite the potential scaling, many reactive atom transfer trajectories (elementary processes) pass through the vicinity of the minimum energy path. Furthermore, we demonstrate that the method can properly imitate the relaxation process owing to the inherent configurational continuity. By comparing the PS-HMC method with other relevant methods, we can conclude that the new method is a unique approach for studying both the dynamic and thermodynamic aspects of chemical processes. [ABSTRACT FROM AUTHOR]

The canonical transformation and Poisson theory for the second-order generalized mechanical systems based on non-standard power-law Lagrangians are studied. First, the Euler–Lagrange equations and the Hamilton canonical equations for the second-order generalized mechanics with the power-law Lagrangians are established. Second, the canonical transformation theory of the systems is studied by establishing the relationship between old and new variables. Four basic forms of canonical transformation are given, and the transformation formulas in each case are derived. Third, the algebraic structure of the dynamical equations of the systems is studied, and the corresponding Poisson theory is established. Finally, the corresponding examples are presented to illustrate the application of the results we obtained. [ABSTRACT FROM AUTHOR]

The description of dynamics for high-energy particles requires an application of the special relativity theory framework, and analysis of properties of the corresponding equations of motion is very important. Here, we analyze Hamilton equations of motion in the limit of weak external field when potential satisfies the condition 2 V (q) ≪ m c 2. We formulate very strong necessary integrability conditions for the case when the potential is a homogeneous function of coordinates of integer non-zero degrees. If Hamilton equations are integrable in the Liouville sense, then eigenvalues of the scaled Hessian matrix γ − 1 V ″ (d) at any non-zero solution d of the algebraic system V ′ (d) = γ d must be integer numbers of appropriate form depending on k. As it turns out, these conditions are much stronger than those for the corresponding non-relativistic Hamilton equations. According to our best knowledge, the obtained results are the first general integrability necessary conditions for relativistic systems. Moreover, a relation between the integrability of these systems and corresponding non-relativistic systems is discussed. The obtained integrability conditions are very easy to use because the calculations reduce to linear algebra. We show their strength in the example of Hamiltonian systems with two degrees of freedom with polynomial homogeneous potentials. It seems that the only integrable relativistic systems with such potentials are those depending only on one coordinate or having a radial form. [ABSTRACT FROM AUTHOR]

We study propagation of high-frequency wave packets along a large-scale background wave, which evolves according to dispersionless hydrodynamic equations for two variables (fluid density and flow velocity). Influence of the wave packet on evolution of the background wave is neglected, so the large-scale evolution can be found independently of the wave packet's motion. At the same time, propagation of the packet depends in an essential way on the background wave, and it can be considered in a framework of the geometric optics approximation with the use of Hamilton equations for the carrier wave number and the mean co-ordinate of the packet. We derive equations for the carrier wave number as a function of the parameters, which describe the background wave. When they are solved, the path of the packet can be found by simple integration of the Hamilton equation. The theory is illustrated by its application to the problem of propagation of wave packets along expanding a large-scale wave, in which evolution is described by the shallow water equations. In particular, they correspond to the dispersionless limit of the defocusing nonlinear Schrödinger equation, and then the expanding wave can be considered as an expanding cloud of the Bose–Einstein condensate. Reflection of wave packets from upstream flows and their propagation along stationary flows are also discussed. The analytical solutions found for these particular cases agree very well with an exact numerical solution of the nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

A combined experimental/theoretical study of the electron paramagnetic resonance (EPR) centers in irradiated β-Ga2O3 is presented. Four EPR spectra, two S = 1/2 and two S = 1, are observed after high-energy proton or electron irradiation. Three of them have been reported before in neutron irradiated samples. One of the S = 1/2 spectra (EPR1) can be observed at room temperature and below and is characterized by the spin Hamiltonian parameters gb = 2.0313, gc = 2.0079, and ga* = 2.0025 and a quasi-isotropic hyperfine interaction with two equivalent Ga neighbors of ∼14 G on 69Ga and correspondingly ∼18 G on 71Ga in their natural abundances. The second (EPR2) is observed after photoexcitation (with a threshold of 2.8 eV) at low temperature and is characterized by gb = 2.0064, gc = 2.0464, and ga* = 2.0024 and a quasi-isotropic hyperfine interaction with two equivalent Ga neighbors of 10 G (for 69Ga). A spin S = 1 spectrum with a similar g-tensor and a 50% reduced hyperfine splitting accompanies each of these, which is indicative of a defect of two weakly coupled S = 1/2 centers. Density functional theory calculations of the magnetic resonance fingerprint (g-tensor and hyperfine interaction) of a wide variety of native defect models and their complexes are carried out to identify these EPR centers in terms of specific defect configurations. The EPR1 center is proposed to correspond to a complex of two tetrahedral VGa1 with an interstitial Ga in between them and oriented in a specific direction in the crystal. This model was previously shown to have lower energy than the simple tetrahedral Ga vacancy and has a 2−/3− transition level higher than other VGa related models, which would explain why the other ones are already in their diamagnetic 3− state and are thus not observed if the Fermi level is pinned approximately at this level. The EPR2 spectra (S = 1/2 as well as the related S = 1) are proposed to correspond to the octahedral VGa2 in which the spin is located on an oxygen off the defect's mirror plane and has a tilted spin density. Models based on self-trapped holes and oxygen interstitials are ruled out because they would have hyperfine interaction with more than two Ga nuclei and because they cannot support a corresponding S = 1 center. [ABSTRACT FROM AUTHOR]

A combined experimental/theoretical study of the electron paramagnetic resonance (EPR) centers in irradiated β-Ga2O3 is presented. Four EPR spectra, two S = 1/2 and two S = 1, are observed after high-energy proton or electron irradiation. Three of them have been reported before in neutron irradiated samples. One of the S = 1/2 spectra (EPR1) can be observed at room temperature and below and is characterized by the spin Hamiltonian parameters gb = 2.0313, gc = 2.0079, and ga* = 2.0025 and a quasi-isotropic hyperfine interaction with two equivalent Ga neighbors of ∼14 G on 69Ga and correspondingly ∼18 G on 71Ga in their natural abundances. The second (EPR2) is observed after photoexcitation (with a threshold of 2.8 eV) at low temperature and is characterized by gb = 2.0064, gc = 2.0464, and ga* = 2.0024 and a quasi-isotropic hyperfine interaction with two equivalent Ga neighbors of 10 G (for 69Ga). A spin S = 1 spectrum with a similar g-tensor and a 50% reduced hyperfine splitting accompanies each of these, which is indicative of a defect of two weakly coupled S = 1/2 centers. Density functional theory calculations of the magnetic resonance fingerprint (g-tensor and hyperfine interaction) of a wide variety of native defect models and their complexes are carried out to identify these EPR centers in terms of specific defect configurations. The EPR1 center is proposed to correspond to a complex of two tetrahedral VGa1 with an interstitial Ga in between them and oriented in a specific direction in the crystal. This model was previously shown to have lower energy than the simple tetrahedral Ga vacancy and has a 2−/3− transition level higher than other VGa related models, which would explain why the other ones are already in their diamagnetic 3− state and are thus not observed if the Fermi level is pinned approximately at this level. The EPR2 spectra (S = 1/2 as well as the related S = 1) are proposed to correspond to the octahedral VGa2 in which the spin is located on an oxygen off the defect's mirror plane and has a tilted spin density. Models based on self-trapped holes and oxygen interstitials are ruled out because they would have hyperfine interaction with more than two Ga nuclei and because they cannot support a corresponding S = 1 center. [ABSTRACT FROM AUTHOR]

We demonstrate for the multi-level spin-boson (MLSB) Hamiltonian, typically used to describe biological light-harvesting, that the distinction between quantum and classical dynamics is determined entirely by the thermal environment. In particular, any MLSB model featuring classical interactions with a classical bath is exactly equivalent in its absorption and energy transfer dynamics to a classical model involving coupled harmonic oscillators. This result holds in the linear response regime for both pulsed and incoherent excitation. In the biological context, this finding highlights the centrality of vibrational dynamics in determining the "quantumness" of photosynthetic light-harvesting, particularly in the creation of the photosynthetic energy funnel where excitation energy concentrates near the reaction center via a series of downhill energy transfer events. These findings support the idea that this energy funnel is exclusively quantum-mechanical in origin, although it need not rely on entanglement. [ABSTRACT FROM AUTHOR]

A derivation of fourth-order vibrational perturbation theory (VPT4) based on the Watson Hamiltonian in dimensionless rectilinear normal coordinates is presented. Terms that are linear and cubic in the (nk + ½), with nk being the zeroth-order harmonic oscillator quantum numbers, appear in fourth order and extend the much simpler second-order vibrational perturbation theory model. The rather involved expressions for the fourth-order terms are derived with Rayleigh-Schröodinger perturbation theory, the process of verifying their correctness is described, and a computer code to generate the VPT4 constants from the potential energy surface derivatives is provided. The paper concludes with numerical examples featuring the H2O, Si2C, and cyclic-C3H2 molecules. [ABSTRACT FROM AUTHOR]

We consider a two-dimensional rigid rotator system coupled to a two-dimensional heat bath. The Caldeira-Leggett (Brownian) model for the rotator and the spin-Boson model have been used to describe such systems, but they do not possess rotational symmetry, and they cannot describe the discretized rotational bands in absorption and emission spectra that have been found experimentally. Here, to address this problem, we introduce a rotationally invariant system-bath (RISB) model that is described by two sets of harmonic-oscillator baths independently coupled to the rigid rotator as sine and cosine functions of the rotator angle. Due to a difference in the energy discretization of the total Hamiltonian, the dynamics described by the RISB model differ significantly from those described by the rotational Caldeira-Legget model, while both models reduce to the Langevin equation for a rotator in the classical limit. To demonstrate this point, we compute the rotational absorption spectrum defined by the linear response function of a rotator dipole. For this purpose, we derive a quantum master equation for the RISB model in the high-temperature Markovian case. We find that the spectral profiles of the calculated signals exhibit a transition from quantized rotational bands to a single peak after spectrum collapse. This is a significant finding because previous approaches cannot describe such phenomena in a unified manner. [ABSTRACT FROM AUTHOR]

For a perturbed quantum system initially in the ground state, the coefficient ck(t) of excited state k in the time-dependent wave function separates into adiabatic and nonadiabatic terms. The adiabatic term ak(t) accounts for the adjustment of the original ground state to form the new ground state of the instantaneous Hamiltonian H(t), by incorporating excited states of the unperturbed Hamiltonian H0 without transitions; ak(t) follows the adiabatic theorem of Born and Fock. The nonadiabatic term bk(t) describes excitation into another quantum state k; bk(t) is obtained as an integral containing the time derivative of the perturbation. The true transition probability is given by bk(t) 2, as first stated by Landau and Lifshitz. In this work, we contrast bk(t) 2 and ck(t) 2. The latter is the norm-square of the entire excited-state coefficient which is used for the transition probability within Fermi’s golden rule. Calculations are performed for a perturbing pulse consisting of a cosine or sine wave in a Gaussian envelope. When the transition frequency ωk0 is on resonance with the frequency ω of the cosine wave, bk(t) 2 and ck(t) 2 rise almost monotonically to the same final value; the two are intertwined, but they are out of phase with each other. Off resonance (when ωk0 ≠ ω), bk(t) 2 and ck(t) 2 differ significantly during the pulse. They oscillate out of phase and reach different maxima but then fall off to equal final values after the pulse has ended, when ak(t) ≡ 0. If ωk0 < ω, bk(t) 2 generally exceeds ck(t) 2, while the opposite is true when ωk0 > ω. While the transition probability is rising, the midpoints between successive maxima and minima fit Gaussian functions of the form a exp[−b(t − d)2]. To our knowledge, this is the first analysis of nonadiabatic transition probabilities during a perturbing pulse. [ABSTRACT FROM AUTHOR]

Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantum mechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the high cost of repetitive QM computations, the slow sampling even for the MM part in those cases where a system under investigation has a complex dynamics, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of "bottom-up" coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantum mechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion, and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed. [ABSTRACT FROM AUTHOR]

We study motion of dark solitons in a non-uniform one-dimensional flow of a Bose–Einstein condensate. Our approach is based on Hamiltonian mechanics applied to the particle-like behavior of dark solitons in a slightly non-uniform and slowly changing surrounding. In one-dimensional geometry, the condensate's wave function undergoes the jump-like behavior across the soliton, and this leads to generation of the counterflow in the background condensate. For a correct description of soliton's dynamics, the contributions of this counterflow to the momentum and energy of the soliton are taken into account. The resulting Hamilton equations are reduced to the Newton-like equation for the soliton's path, and this Newton equation is solved in several typical situations. The analytical results are confirmed by numerical calculations. [ABSTRACT FROM AUTHOR]

Complete Active Space SCF (CASSCF) theory may provide poor 0th order descriptions due to the lack of dynamic correlation. The most popular post-CASSCF approaches for recovering dynamic correlation are methods which keep the configuration interaction coefficients fixed at the CASSCF level and use internal contraction. This may result in severe inaccuracies where the wavefunction changes considerably under the influence of dynamic correlation. In this paper, we propose and compare several variants of a straightforward method of the "perturb-then-diagonalize" type that is aimed at keeping this balance while remaining computationally tractable and numerically stable. The method is loosely based on the theory of intermediate Hamiltonians and has been given the acronym "dynamic correlation dressed CAS" (DCD-CAS), with the second-order treatment, DCD-CAS(2), being the most practically useful member of the family. The dynamic correlation energy is treated to second order with a 0th order Hamiltonian based on Dyall's Hamiltonian. The method is orbitally invariant with respect to unitary transformations in the occupied, active, and virtual subspaces. It yields the ground- and low-lying excited states at the same time. Detailed numerical evaluations show that DCD-CAS(2) is superior to NEVPT2 for the difficult situations mentioned above while being very close to it when CASSCF provides a good 0th order description. [ABSTRACT FROM AUTHOR]

The RMF (Rotating Magnetic Field) code is designed to calculate the motion of a charged particle in a given electromagnetic field. It integrates Hamilton's equations in cylindrical coordinates using an adaptive predictor-corrector double-precision variable-coefficient ordinary differential equation solver for speed and accuracy. RMF has multiple capabilities for the field. Particle motion is initialized by specifying the position and velocity vectors. The six-dimensional state vector and derived quantities are saved as functions of time. A post-processing graphics code, XDRAW, is used on the stored output to plot up to 12 windows of any two quantities using different colors to denote successive time intervals. Multiple cases of RMF may be run in parallel and perform data mining on the results. Recent features are a synthetic diagnostic for simulating the observations of charge-exchange-neutral energy distributions and RF grids to explore a Fermi acceleration parallel to static magnetic fields. [ABSTRACT FROM AUTHOR]

The incorporation of the geometric phase in single-state adiabatic dynamics near a conical intersection (CI) seam has so far been restricted to molecular systems with high symmetry or simple model Hamiltonians. This is due to the fact that the ab initio determined derivative coupling (DC) in a multi-dimensional space is not curl-free, thus making its line integral path dependent. In a recent work [C. L. Malbon et al., J. Chem. Phys. 145, 234111 (2016)], we proposed a new and general approach based on an ab initio determined diabatic representation consisting of only two electronic states, in which the DC is completely removable, so that its line integral is path independent in the simply connected domains that exclude the CI seam. Then with the CIs included, the line integral of the single-valued DC can be used to construct the complex geometry-dependent phase needed to exactly eliminate the double-valued character of the real-valued adiabatic electronic wavefunction. This geometry-dependent phase gives rise to a vector potential which, when included in the adiabatic representation, rigorously accounts for the geometric phase in a system with an arbitrary locus of the CI seam and an arbitrary number of internal coordinates. In this work, we demonstrate this approach in a three-dimensional treatment of the tunneling facilitated dissociation of the S1 state of phenol, which is affected by a Cs symmetry allowed but otherwise accidental seam of CI. Here, since the space is three-dimensional rather than two-dimensional, the seam is a curve rather than a point. The nodal structure of the ground state vibronic wavefunction is shown to map out the seam of CI. [ABSTRACT FROM AUTHOR]

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the △MPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except △MPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 but converges at the full-configurationinteraction (FCI) limit at n = ∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or △MPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of △MPn and MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams. [ABSTRACT FROM AUTHOR]

The use of a highly localized plasmonic field has enabled us to achieve sub-nanometer resolution of Raman images for single molecules. The inhomogeneous spatial distribution of plasmonic field has become an important factor that controls the interaction between the light and the molecule. We present here a gauge invariant interaction Hamiltonian (GIIH) to take into account the non-uniformity of the electromagnetic field distribution in the non-relativistic regime. The theory has been implemented for both resonant and nonresonant Raman processes within the sum-over-state framework. It removes the gauge origin dependence in the phenomenologically modified interaction Hamiltonian (PMIH) employed in previous studies. Our calculations show that, in most resonant cases, the Raman images from GIIH are similar to those from PMIH when the origin is set to the nuclear charge center of the molecule. In the case of nonresonant Raman images, distinct differences can be found from two different approaches, while GIIH calculations provide more details and phase information of the images. Furthermore, the results from GIIH calculations are more stable with respect to the computational parameters. Our results not only help to correctly simulate the resonant and nonresonant Raman images of single molecules but also lay the foundation for developing gauge invariant theory for other linear and nonlinear optical processes under the excitation of non-uniform electromagnetic field. [ABSTRACT FROM AUTHOR]

The transport of polarons above the mobility threshold in organic and inorganic polymers is theoretically investigated in the framework of a one-dimensional tight-binding model that includes lattice relaxation. The computational approach is based on parameters for which the model Hamiltonian suitably describes different polymer lattices in the presence of external electric fields. Our findings show that, above critical field strengths, a dissociated polaron moves through the polymer lattice as a free electron performing Bloch oscillations. These critical electric fields are considerably smaller for inorganic lattices in comparison to organic polymers. Interestingly, for inorganic lattices, the free electron propagates preserving charge and spin densities' localization which is a characteristic of a static polaron. Moreover, in the turning points of the spatial Bloch oscillations, transient polaron levels are formed inside the band gap, thus generating a fully characterized polaron structure. For the organic case, on the other hand, no polaron signature is observed: neither in the shape of the distortion-those polaron profile signatures are absent-nor in the energy levels-as no such polaron levels are formed during the simulation. These results solve controversial aspects concerning Bloch oscillations recently reported in the literature and may enlighten the understanding about the charge transport mechanism in polymers above their mobility edge. [ABSTRACT FROM AUTHOR]

Several symplectic splitting methods of orders four and six are presented for the step-by-step time numerical integration of the Schrödinger equation when the Hamiltonian is a general explicitly time-dependent real operator. They involve linear combinations of the Hamiltonian evaluated at some intermediate points. We provide the algorithm and the coefficients of the methods, as well as some numerical examples showing their superior performance with respect to other available schemes. [ABSTRACT FROM AUTHOR]

Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize dynamically, thereby reducing the magnitude of the interaction. Exchange integrals of molecular orbitals are not correlated. The modified Coulomb interactions are used in single-determinant or configuration interaction calculations. The objective is to account for dynamical correlation effects without explicitly introducing higher spherical harmonic functions into the molecular orbital basis. Molecular orbital densities are decomposed into a distribution of spherical components that conserve the charge and each of the interacting components is considered as a two-electron wavefunction embedded in the system acted on by an average field Hamiltonian plus r-112. A method of avoiding redundancy is described. Applications to atoms, negative ions, and molecules representing different types of bonding and spin states are discussed. [ABSTRACT FROM AUTHOR]

First, he claims that the form used for Hamiltonian HT ht in Eq. (2) of Ref. [1] is not a correct Hamiltonian for Eq. (1) of Ref. [1]. 2 and we can see that the discrete soliton can maintain its shape and location quite well during propagation up to HT ht . Because in this case, the central amplitudes HT ht of the discrete solitons are low, so these two curves are practically the same. [Extracted from the article]

We propose a new unified theoretical framework to construct equivalent representations of the multistate Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional Hamiltonian onto an F+1 dimensional space, creation and annihilation operators are defined such that the F+1 dimensional space is complete for any combined excitation. Commutation and anti-commutation relations are then naturally derived, which show that the underlying degrees of freedom are neither bosons nor fermions. This sets the scene for developing equivalent expressions of the Hamiltonian operator in quantum mechanics and their classical/semiclassical counterparts. Six mapping models are presented as examples. The framework also offers a novel way to derive such as the well-known Meyer-Miller model. [ABSTRACT FROM AUTHOR]

A new truncation scheme for non-orthogonal antisymmetrized products of interacting geminals (APIG) is introduced based on antisymmetrized products of strongly orthogonal geminals (APSG). This wavefunction hierarchy of interacting geminals (IG) allows us to gradually increase the accuracy at which the ground state of a seniority-zero Hamiltonian can be estimated, ranging from APSG up to approximation-free APIG. Mathematical expressions for the lowest four orders (IG0, IG1, IG2, and IG3) are given explicitly and the computational cost to evaluate their transition density matrix is verified to scale only cubically with system size. Exemplary numerical calculations indicate that already a very early truncation level leads to results virtually identical to APIG. [ABSTRACT FROM AUTHOR]

In this work, we have studied the electron localization due to a random distribution of side-attached linear organic molecules on graphene nanoribbons. By using the Green's function formalism within a tight binding Hamiltonian approximation and considering an Anderson-like disorder, we have calculated the conductance of the systems and the corresponding localization lengths. Our results show that the localization length strongly depends on the molecular concentration and on the length of the molecules, effects that are robust for different ribbon widths. These results suggest possible applications in molecular detectors or sensors based on graphene nanoribbons. [ABSTRACT FROM AUTHOR]

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is implemented in the interaction picture to allow a more effective description of correlation effects. It is shown that the artificial correlation present in the original Schrödinger picture can be removed with an appropriate choice of the zeroth-order Hamiltonian. Thereby, operators in the interaction picture are obtained through time-dependent unitary transformations, which have negligible computational cost compared with other parts of the ML-MCTDH algorithm. The efficiency of the method is demonstrated by application to a model of vibrationally coupled charge transport in molecular junctions. [ABSTRACT FROM AUTHOR]

Quantum interference in scattering from a potential offset is investigated in narrow strips of two-dimensional systems described by the Bernevig-Hughes-Zhang Hamiltonian. Attention is focused on the situations where the transmission in the scattering region takes place around the Dirac point of topological insulators when the hybridization energy gap is eliminated by utilizing transverse interference. Apart from conventional periodic transmission modulation that takes place when the length of the potential offset region is varied, resonant disappearances of reflection occur for short potential offsets. The anomalous resonance appears not only for the four-band Hamiltonian but also for the two-band Hamiltonian, manifesting the generality of the phenomenon. Evanescent-like waves excited around the potential steps are indicated to be responsible for the anomalous behavior. The interference states can couple with each other and generic reduction in the amplitude of transmission modulation occurs upon coupling with the periodic modulation. [ABSTRACT FROM AUTHOR]

The vibrational spectrum of ammonia has received an enormous amount of attention due to its potential prevalence in hot exo-planet atmospheres and persistent challenges in assigning and modeling highly excited and often highly perturbed states. Effective Hamiltonian models face challenges due to strong coupling between the large amplitude inversion and the other small amplitude vibrations. To date, only the ground and ν2 positions could be modeled to experimental accuracy using effective Hamiltonians. Several previous attempts to analyze the 2ν2 and 4 energy levels failed to model both the microwave and infrared transitions to experimental accuracy. In this work, we performed extensive experimental measurements and data analysis for the 2ν2 and ν4 inversion-rotation and vibrational transitions. We measured 159 new transition frequencies with microwave precision and assigned 1680 new ones from existing Fourier transform spectra recorded in Synchrotron SOLEIL. The newly assigned data significantly expand the range of assigned quantum numbers; combined with all the previously published high-resolution data, the 2ν2 and ν4 states are reproduced to experimental accuracy using a global model described here. Achieving experimental accuracy required inclusion of a number of terms in the effective Hamiltonian that were neglected in previous work. These terms have also been neglected in the analysis of states higher than 2ν2 and ν4 suggesting that the inversion-rotation-vibration spectrum of ammonia may be far more tractable to effective Hamiltonians than previously believed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a pruned, nondirect product multi-configuration time dependent Hartree (MCTDH) method for solving the Schrödinger equation. MCTDH uses optimized 1D basis functions, called single particle functions, but the size of the standard direct product MCTDH basis scales exponentially with D, the number of coordinates. We compare the pruned approach to standard MCTDH calculations for basis sizes small enough that the latter are possible and demonstrate that pruning the basis reduces the CPU cost of computing vibrational energy levels of acetonitrile (D = 12) by more than two orders of magnitude. Using the pruned method, it is possible to do calculations with larger bases, for which the cost of standard MCTDH calculations is prohibitive. Pruning the basis complicates the evaluation of matrix-vector products. In this paper, they are done term by term for a sum-of-products Hamiltonian. When no attempt is made to exploit the fact that matrices representing some of the factors of a term are identity matrices, one needs only to carefully constrain indices. In this paper, we develop new ideas that make it possible to further reduce the CPU time by exploiting identity matrices. [ABSTRACT FROM AUTHOR]

The 8-band kp Hamiltonian is applied to calculate electronic band structure and material gain in III-V-Bi quantum wells (QWs) grown on GaSb substrates. We analyzed three Bi-containing QWs (GaSbBi, GaInSbBi, and GaInAsSbBi) and different Bi-free barriers (GaSb and AlGaInAsSb), lattice matched to GaSb. Bi-related changes in the electronic band structure of III-V host incorporated into our formalism are based on recent ab-initio calculations for ternary alloys (III-Ga-Bi and IIIIn-Bi) [Polak et al., Semicond. Sci. Technol. 30, 094001 (2015)]. When compared to Bi-free QWs, the analyzed Bi-containing structures show much better quantum confinement in the valence band and also larger redshift of material gain peak per percent of compressive strain. For 8 nm thick GaInSb/GaSb QWs, material gain of the transverse electric (TE) mode is predicted at 2.1 μm for the compressive strain of ϵ = 2% (32% In). The gain peak of the TE mode in 8 nm thick GaSbBi/GaSb QW reaches this wavelength for compressive strain of 0.15% that corresponds to about 5% Bi. It has also been shown that replacing In atoms by Bi atoms in GaInSbBi/GaSb QWs while keeping the same compressive strain (ϵ = 2%) in QW region enhances and shifts gain peak significantly to the longer wavelengths. For 8 nm wide GaInSbBi/GaSb QW with 5% Bi, the gain peak is predicted at around 2.6 lm, i.e., is redshifted by about 400 nm compared to Bi-free QW. For 8 nm wide GaInAsSbSb QWs (80% In, 5% Bi, and ϵ = 2%) with proper AlGaInAsSb barriers, it is possible to achieve large material gain even at 4.0 μm. [ABSTRACT FROM AUTHOR]

Isotope effects of the H3O-2 anion are investigated. For this, the 24 lowest excited vibrational states of the H3-xDxO-2 complexes, with x = 0-3, are computed using two different Hamiltonians, namely, a 7D reduced-dimensionality one with a numerical representation of the kinetic energy operator (KEO) and a 9D full-dimensionality Hamiltonian with an exact analytic KEO. The computations are carried out with the multiconfiguration time-dependent Hartree method. The obtained results show that bridge and terminal H-D exchange cause a variation in energy with or without a rearrangement of states. A clear rearrangement of fundamental modes is observed in bridge H-D exchange of the H3O-2 complex, where the frequency of bridge hydrogen stretching (z) is strongly lowered by substitution. The isotope effects show that rotation (Φ), rocking (u1 + u2), wagging (u1 - u2), and O-O stretch (R) modes are sensitive to terminal H-D exchange, while the bridge-atom bending (x,y) and stretch (z) modes are sensitive to bridge H-D exchange. An influence coefficient, which measures the influence of an excitation of one mode on the various 1D reduced densities, is defined and analyzed in detail. It is shown that the D3O-2 complex is more strongly correlated or coupled than the other isotopologues. [ABSTRACT FROM AUTHOR]

We present a critical analysis of the popular fragment-orbital density-functional theory (FO-DFT) scheme for the calculation of electronic coupling values. We discuss the characteristics of different possible formulations or "flavors" of the scheme which differ by the number of electrons in the calculation of the fragments and the construction of the Hamiltonian. In addition to two previously described variants based on neutral fragments, we present a third version taking a different route to the approximate diabatic state by explicitly considering charged fragments. In applying these FO-DFT flavors to the two molecular test sets HAB7 (electron transfer) and HAB11 (hole transfer), we find that our new scheme gives improved electronic couplings for HAB7 (-6.2% decrease in mean relative signed error) and greatly improved electronic couplings for HAB11 (-15.3% decrease in mean relative signed error). A systematic investigation of the influence of exact exchange on the electronic coupling values shows that the use of hybrid functionals in FO-DFT calculations improves the electronic couplings, giving values close to or even better than more sophisticated constrained DFT calculations. Comparing the accuracy and computational cost of each variant, we devise simple rules to choose the best possible flavor depending on the task. For accuracy, our new scheme with chargedfragment calculations performs best, while numerically more efficient at reasonable accuracy is the variant with neutral fragments. [ABSTRACT FROM AUTHOR]

We report remarkable results due to the coupling between the magnetization and the electric field induced polarization in EuTiO3. Using a microscopic model Hamiltonian to describe the three coupled sublattices, Eu-(spin-up), Eu-(spin-down), and Ti-(moment), the spin flop and spin reorientation phase transitions were described with and without the electric-magnetic coupling interaction. The external electric field can be used to tune the temperature of the spin reorientation phase transition TSR=TSR(E). When the TSR is tuned around the EuTiO3—Néel temperature (TN=5.5K), an outstanding effect emerges in which EuTiO3 releases heat under magnetic field change. The electric field controlling the spin reorientation transition and the endo-exothermic processes are discussed through the microscopic interactions model parameters. [ABSTRACT FROM AUTHOR]

We report remarkable results due to the coupling between the magnetization and the electric field induced polarization in EuTiO3. Using a microscopic model Hamiltonian to describe the three coupled sublattices, Eu-(spin-up), Eu-(spin-down), and Ti-(moment), the spin flop and spin reorientation phase transitions were described with and without the electric-magnetic coupling interaction. The external electric field can be used to tune the temperature of the spin reorientation phase transition TSR=TSR(E). When the TSR is tuned around the EuTiO3—Néel temperature (TN=5.5K), an outstanding effect emerges in which EuTiO3 releases heat under magnetic field change. The electric field controlling the spin reorientation transition and the endo-exothermic processes are discussed through the microscopic interactions model parameters. [ABSTRACT FROM AUTHOR]

We develop a machine learning framework that can be applied to data sets derived from the trajectories of Hamilton's equations. The goal is to learn the phase space structures that play the governing role for phase space transport relevant to particular applications. Our focus is on learning reactive islands in two degrees-of-freedom Hamiltonian systems. Reactive islands are constructed from the stable and unstable manifolds of unstable periodic orbits and play the role of quantifying transition dynamics. We show that the support vector machines are an appropriate machine learning framework for this purpose as it provides an approach for finding the boundaries between qualitatively distinct dynamical behaviors, which is in the spirit of the phase space transport framework. We show how our method allows us to find reactive islands directly in the sense that we do not have to first compute unstable periodic orbits and their stable and unstable manifolds. We apply our approach to the Hénon–Heiles Hamiltonian system, which is a benchmark system in the dynamical systems community. We discuss different sampling and learning approaches and their advantages and disadvantages. [ABSTRACT FROM AUTHOR]

We present two improvements to the tight-binding approximation of time-dependent density functional theory (TD-DFTB): First, we add an exact Hartree-Fock exchange term, which is switched on at large distances, to the ground state Hamiltonian and similarly to the coupling matrix that enters the linear response equations for the calculation of excited electronic states. We show that the excitation energies of charge transfer states are improved relative to the standard approach without the long-range correction by testing the method on a set of molecules from the database in Peach et al. [J. Chem. Phys. 128, 044118 (2008)] which are known to exhibit problematic charge transfer states. The degree of spatial overlap between occupied and virtual orbitals indicates where TD-DFTB and long-range corrected TD-DFTB (lc-TD-DFTB) can be expected to produce large errors. Second, we improve the calculation of oscillator strengths. The transition dipoles are obtained from Slater Koster files for the dipole matrix elements between valence orbitals. In particular, excitations localized on a single atom, which appear dark when using Mulliken transition charges, acquire a more realistic oscillator strength in this way. These extensions pave the way for using lc-TD-DFTB to describe the electronic structure of large chromophoric polymers, where uncorrected TD-DFTB fails to describe the high degree of conjugation and produces spurious low-lying charge transfer states. [ABSTRACT FROM AUTHOR]

It was suggested that single-layer MoS2 at the 1T' phase is a topological insulator whose electronic structure can be modulated by a vertical electric field for field-effect transistor (FET) applications [X. Qian, J. Liu, L. Fu, and J. Li, Science 346, 1344 (2014)]. In this work, performance potential of FETs based on vertical field modulation of the topological edge states is assessed by using quantum transport device simulations. To perform efficient device simulations, a phenomenological Hamiltonian is first proposed and validated to capture the effects of electric fields. Because the ON-state conductance is determined by transport through gapless edge states with a long scattering mean free path and the OFF-state conductance by transport through the gapped bulk states, the ON/OFF ratio is sensitive to the channel length, which is different from conventional FETs. Although a high vertical electric field is required to modulate the topological edge state, a reasonably small subthreshold swing of 131 mV/dec can still be achieved for a practical value of the gate insulator thickness. [ABSTRACT FROM AUTHOR]

We report the observation of eigenstates that embody large-amplitude, local-bending vibrational motion in acetylene by stimulated emission pumping spectroscopy via vibrational levels of the S1 state involving excitation in the non-totally symmetric bending modes. The Nb = 14 level, lying at 8971.69 cm-1 (J = 0), is assigned on the basis of degeneracy due to dynamical symmetry breaking in the local-mode limit. The level pattern for the Nb = 16 level, lying at 10 218.9 cm-1, is consistent with expectations for increased separation of l = 0 and 2 vibrational angular momentum components. Increasingly poor agreement between our observations and the predicted positions of these levels highlights the failure of currently available normal mode effective Hamiltonian models to extrapolate to regions of the potential energy surface involving large-amplitude displacement along the acetylene vinylidene isomerization coordinate. [ABSTRACT FROM AUTHOR]

An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles-doubles-perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the dependence of correlation and binding energies on the magnetic field. [ABSTRACT FROM AUTHOR]

Many people in the materials science and solid-state community are familiar with the acronym "DFT+U." For those less familiar, this technique uses ideas from model Hamiltonians that permit the description of both metals and insulators to address problems of electron over-delocalization in practical implementations of density functional theory (DFT). Exchange-correlation functionals in DFT are often described as belonging to a hierarchical "Jacob's ladder" of increasing accuracy in moving from local to non-local descriptions of exchange and correlation. DFT+U is not on this "ladder" but rather acts as an "elevator" because it systematically tunes relative energetics, typically on a localized subshell (e.g., d or f electrons), regardless of the underlying functional employed. However, this tuning is based on a metric of the local electron density of the subshells being addressed, thus necessitating physical or chemical or intuition about the system of interest. I will provide a brief overview of the history of how DFT+U came to be starting from the origin of the Hubbard and Anderson model Hamiltonians. This history lesson is necessary because it permits us to make the connections between the "Hubbard U" and fundamental outstanding challenges in electronic structure theory, and it helps to explain why this method is so widely applied to transition-metal oxides and organometallic complexes alike. [ABSTRACT FROM AUTHOR]

We develop a first principles theoretical description of femtosecond double-pump single-molecule signals of molecular aggregates. We incorporate all singly excited electronic states and vibrational modes with significant exciton-phonon coupling into a system Hamiltonian and treat the ensuing system dynamics within the Davydov D1 Ansatz. The remaining intra- and inter-molecular vibrational modes are treated as a heat bath and their effect is accounted for through lineshape functions. We apply our theory to simulate single-molecule signals of the light harvesting complex II. The calculated signals exhibit pronounced oscillations of mixed electron-vibrational (vibronic) origin. Their periods decrease with decreasing exciton-phonon coupling. [ABSTRACT FROM AUTHOR]

In this paper, we study the exact solitary wave solutions, periodic wave solutions, and bounded rational function solution of the high-order nonlinear Schrödinger equation and the evolutional relationships between the solitary and periodic wave solutions dependent on the Hamilton energy of their amplitude. First, based on the theory and the method of planar dynamical systems, we give a detailed qualitative analysis of the planar dynamical systems corresponding to the amplitude of traveling wave solutions. Then, based on the first integral of the system, we obtain the exact solitary wave solutions, periodic wave solutions, and bounded rational function solution of the equation in various forms by the analysis method, the integral technique, and proper transformation and establish the relationship between the solutions and the Hamilton energy of their amplitude. Furthermore, we discuss the evolutional relationships between the solitary and periodic wave solutions and reveal that the solitary and periodic wave solutions of the equation are essentially determined by the energy change in the Hamilton system corresponding to their amplitude. Finally, we give some diagrams that demonstrate the evolution from periodic wave solutions to solitary wave solutions when Hamilton energy changes. [ABSTRACT FROM AUTHOR]

We consider propagation of high-frequency wave packets along a smooth evolving background flow whose evolution is described by a simple-wave type of solutions of hydrodynamic equations. In geometrical optics approximation, the motion of the wave packet obeys the Hamilton equations with the dispersion law playing the role of the Hamiltonian. This Hamiltonian depends also on the amplitude of the background flow obeying the Hopf-like equation for the simple wave. The combined system of Hamilton and Hopf equations can be reduced to a single ordinary differential equation whose solution determines the value of the background amplitude at the location of the wave packet. This approach extends the results obtained in the paper by Congy et al. [J. Fluid Mech. 875, 1145 (2019)] for the rarefaction background flow to arbitrary simple-wave type background flows. The theory is illustrated by its application to waves obeying the KdV equation. [ABSTRACT FROM AUTHOR]

An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH+ (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the nonrelativistic relation remains valid within 2% even for the heavy HI, IF, and XeH+ systems. Only for the sixth-row Rn atom a significant deviation of this relation is found. [ABSTRACT FROM AUTHOR]