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Host–guest binding plays a crucial role in the functionality of various systems, and its efficiency is often quantified using the binding free energy, which represents the free-energy difference between the bound and dissociated states. Here, we propose a methodology to compute the binding free energy based on the energy representation (ER) theory of solution, which enables us to evaluate the free-energy difference between the systems of interest with the molecular dynamics (MD) simulations. Unlike the other free-energy methods, such as the Bennett acceptance ratio (BAR), the ER theory does not require the MD simulations for hypothetical intermediate states connecting the systems of interest, leading to reduced computational costs. By constructing the thermodynamic cycle of the binding process that is suitable for the ER theory, a robust calculation of the binding free energy is realized. We apply the present method to the self-association of N-methylacetamide in different solvents and the binding of aspirin to β-cyclodextrin (CD) in water. In the former case, the present method estimates that the binding free energy decreases as the solvent polarity decreases. This trend is consistent with the experimental finding. For the latter system, the binding free energies for the two representative CD–aspirin bound complexes, primary (P) and secondary (S) complexes, are estimated to be −5.2 ± 0.1 and −5.03 ± 0.09 kcal mol−1, respectively. These values are satisfactorily close to those from the BAR method [−4.2 ± 0.2 and −4.1 ± 0.2 kcal mol−1 for P and S, respectively]. Furthermore, the interaction-energy component analysis reveals that the van der Waals interaction between aspirin and CD dominantly contributes to the stabilization of the bound complexes, which is in harmony with the well-known binding mechanism in the CD systems. [ABSTRACT FROM AUTHOR]

We report a plasmonic–dielectric metasurface that offers dynamic control over chiroptical properties, adjustable Q-factors, and inter-band chirality manipulation through multiple symmetry-breaking mechanisms. By controlling chiral quasi-bound states in the continuum (BIC) modes and Fano resonances, we enable hybridized and independently tunable spectral responses, offering precise control over resonance amplitude, polarization sensitivity, and refractive index sensing with high flexibility. Chirality is induced by rotating silicon nanofins on a dielectric spacer with a gold backplate, enabling tunable chiroptical responses with controllable spectral linewidth and independent or simultaneous dual-wavelength band excitation. We report a novel phenomenon of controlling interplay of chirality between two closely positioned wavelength bands to tailor symmetry breaking for a specific resonant mode (chiral) while preserving symmetry for the other mode (achiral). Additionally, we report the phase-sensitive evolution of Fano resonance from pure reflectance dip when controlled by dielectric spacer height and further demonstrated phase-insensitive control of Fano resonance amplitude. We divided Fano resonance into a distinct spectral peak and dip to improve light manipulation within the metasurface. Our proposed sensor demonstrates sensitivity and a quality factor of about 435 nm/RIU and 3888, respectively. Furthermore, we compared different phenomena (chiral selectivity, quasi-BIC, Fano) and sensing parameter values for different metasurface configurations (including single nanofin and absence of a spacer) and observed that the configuration without a spacer achieved the highest sensitivity of approximately 640 nm/RIU. [ABSTRACT FROM AUTHOR]

A four-dimensional potential energy surface (4D-PES) has been constructed for the N2–OCS complex. The PES is achieved by applying the explicitly correlated coupled cluster method, which incorporates single, double, and perturbative triple excitations [CCSD(T)-F12a], along with the augmented correlation consistent triple zeta (aug-cc-pVTZ) basis set. The rovibrational levels are precisely determined and assigned through bound state calculations and wavefunction analysis. The calculated transition frequencies reproduce the experimental observations accurately, achieving an RMSE of 0.0005 cm−1 for the 23 rotational transitions (J ≤ 6, Ka ≤ 2). The R-φ contour plot of the wave function clearly demonstrates the unambiguous delocalization of the dihedral angle, and the averaged geometry of the ground vibrational state is determined to be non-planar with φ = 90°. To obtain a quantitative analysis of this phenomenon, we expanded the 3H-solution model [Guo et al., J. Quant. Spectrosc. Radiat. Transfer 309 (2023) 108711] from a three-dimensional system (Ar–AgF) to a nine-dimensional system (N2–OCS). Based on this model, the tunneling splitting was calculated to be 0.0822 cm−1, which excellently matches the experimental result of 0.0817 cm−1. The excellent agreement between the theoretical and experimental results suggests that the wavefunction delocalization and out-of-plane motion can be attributed to the tunneling effects in the ground vibrational state. [ABSTRACT FROM AUTHOR]

We report the experimental observation of the delayed fragmentation of the weakly bound dimer Kr2+ produced through the single ionization of Kr2 by a femtosecond laser field. The observed time delay between ionization and fragmentation, which reflects the survival time of the resulting Kr2+, is measured on the microsecond timescale. A detailed analysis of the kinetic energy releases of the ejected fragments and photoelectrons suggests that this delayed fragmentation arises from the radiative decay of the long-lived Kr2+, transitioning from the bound state II(1/2u) to the repulsive state I(1/2g). [ABSTRACT FROM AUTHOR]

We report the experimental observation of the delayed fragmentation of the weakly bound dimer Kr2+ produced through the single ionization of Kr2 by a femtosecond laser field. The observed time delay between ionization and fragmentation, which reflects the survival time of the resulting Kr2+, is measured on the microsecond timescale. A detailed analysis of the kinetic energy releases of the ejected fragments and photoelectrons suggests that this delayed fragmentation arises from the radiative decay of the long-lived Kr2+, transitioning from the bound state II(1/2u) to the repulsive state I(1/2g). [ABSTRACT FROM AUTHOR]

Ab initio molecular dynamics simulations of negatively charged clusters of 2–48 ammonia molecules were performed to elucidate the electronic stability of the excess electron as a function of cluster size. We show that while the electronic stability of finite temperature clusters increases with cluster size, as few as 5–7 ammonia molecules can bind an excess electron, reaching a vertical binding energy slightly less than half of the bulk value for the largest system studied. These results, which are in agreement with previous studies wherever available, allowed us to analyze the excess electron binding patterns in terms of its radius of gyration and shape anisotropy and provide a qualitative interpretation based on a particle-in-a-spherical-well model. [ABSTRACT FROM AUTHOR]

The study of the behavior of magnetic skyrmions in local magnetic fields' nanometric length-scale has gained increasing interest in recent years due to the theoretical proposal of magnetic skyrmion–superconducting vortex pairs as potential hosts for topologically protected bound states, which hold high promise for applications in quantum computing. From a magnetic interaction point-of-view, the key interest lies in understanding the skyrmion dynamics triggered by the magnetic energy landscape generated by the superconducting vortex. Here, we present a micromagnetic study of the dynamics of nanometric skyrmions inside a Gaussian magnetic field profile, which is used as a simplified version of the vortex magnetic flux. On the one hand, our calculations show that local non-linear magnetic fields can be very effective in controlling the dynamics of magnetic skyrmions; in particular, they offer the appealing possibility to manipulate skyrmions in a two dimensional space. On the other hand, they also show that the dynamics of a skyrmion in a local magnetic field can be manipulated via a uniform external magnetic field without any change in the magnetic field gradient. An analytical expression for the skyrmion velocity is given, and the corresponding microscopic dynamics are confirmed by the micromagnetic simulations. This work is expected to motivate more theoretical and experimental studies of the behavior of magnetic skyrmions in proximity to superconducting vortices. [ABSTRACT FROM AUTHOR]

A bound state in the continuum (BIC) metasurface (MS) was designed to achieve an ultrahigh quality factor(Q factor) using natural hyperbolic materials, such as hexagonal boron nitride. To investigate the structure's dispersion and Q factor, a unit cell of the MS comprising semicircles and rectangles was designed. This MS structure supports symmetry-protected BICs and exhibits a Q factor of approximately 13 000 at 4.43964 × 1013 Hz. By breaking the MS symmetry, the BICs are converted into quasi-BICs, resulting in quasi-BIC resonance with a high Q factor. Further analysis of the reflection spectra and multipole theory indicates that the toroidal dipole (TD) has the most significant influence on the resonance. Thus, the symmetry-protected BIC can be transformed into the TD resonance with a Q factor by breaking symmetry. [ABSTRACT FROM AUTHOR]

The response of a biological network to ligand binding is of crucial importance for regulatory control in various cellular biophysical processes that is achieved with information transmission through the different ligand-bound states of such networks. In this work, we address a vital issue regarding the link between the information content of such network states and the experimentally measurable binding statistics. Several fundamental networks of cooperative ligand binding, with the bound states being adjacent in time only and in both space and time, are considered for this purpose using the chemical master equation approach. To express the binding characteristics in the language of information, a quantity denoted as differential information index is employed based on the Shannon information. The index, determined for the whole network, follows a linear relationship with (logarithmic) ligand concentration with a slope equal to the size of the system. On the other hand, the variation of Shannon information associated with the individual network states and the logarithmic sensitivity of its slope are shown to have generic forms related to the average binding number and variance, respectively, the latter yielding the Hill slope, the phenomenological measure of cooperativity. Furthermore, the variation of Shannon information entropy, the average of Shannon information, is also shown to be related to the average binding. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Feshbach resonances of high partial waves and the influence of spin–spin (S–S) interaction on ultracold scattering processes. Taking the N a 23 - R b 87 system as an example, we plot the variations of weakly bound state energy and elastic scattering cross section with magnetic field and with collision energy. We find that the number of splittings in high partial wave Feshbach resonances does not strictly conform to the expected l + 1 (l is rotational angular momentum), and the deviation is attributed to the influence of bound states in other channels coupled by S–S interaction. For different ml (the projection of l on the external magnetic field direction), the effects of S–S interaction lead to different scattering patterns in the incident channels. These results reveal the complex features of ultracold scattering processes in high partial waves caused by S–S interaction. [ABSTRACT FROM AUTHOR]

Free molecules undergo processes with photons; in particular, they can undergo photoionization and photodissociation, which are relevant processes in nature and laboratory. Recently, it has been shown that in a cavity, the reverse process of photoionization, namely, electron capture becomes highly probable. The underlying mechanism is the formation of a hybrid resonance state. In this work, we demonstrate that the idea of enhanced reverse processes is more general. We discuss the case of the reverse process of photodissociation, namely, making a molecule out of separate atoms in a cavity. For bound electronic states, the interaction of atoms and molecules with quantum light as realized in cavities is known to give rise to the formation of hybrid light–matter states (usually called polaritons). In the scenarios discussed here, the hybrid light–matter states are resonance (metastable) states, which decay into the continuum of either electrons or of the fragments of a molecule. Resonances can substantially enhance the outcome of processes. In addition to the new resonant mechanism of molecule formation, the impact of the hybrid resonances on the scattering cross section of the atoms can be dramatic. [ABSTRACT FROM AUTHOR]

In this article, significant contributions of non-adiabaticity for the rovibrational bound states up to 25 000 cm−1 and total angular momentum J = 0–20 of H 3 + are investigated. A coupled-perturbed full configuration interaction (CP-FCI) treatment is applied to calculate all couplings between electronic states caused by the nuclear motion. These derivative couplings were evaluated up to the second order by means of a perturbation treatment and include all nuclear Cartesian first and second derivatives of the electronic wavefunctions. In particular, the coupling of special derivatives with respect to r and R in the Jacobi coordinate representation is more significant than thought. The perturbation approach is especially optimal for the treatment of weak non-adiabaticity in case of rovibrational energies in H 3 + and had not been available before for H 3 + or other triatomics. Using exclusively Gaussian basis functions for CP-FCI appears to be sufficient, because explicit correlated wavefunctions are already used for all other potential energy contributions. Our work is an extension of earlier non-adiabatic investigations based on first derivative couplings of electronic states that led to the concept of geometry-dependent effective nuclear masses and which needs only a single potential energy surface for the dynamics. The implementation allows us to include all non-adiabatic effects up to the order of O ( μ − 2 ) , μ being the reduced nuclear mass. Our treatment works for any isotopologue and for the whole potential energy curve or surface. By this treatment, a further reduction in deviations to experimental data for most rovibrational levels to less than 0.1 cm−1 is possible. For the related transition frequencies, 1366 of 1720 known rovibrational transitions in H 3 + have deviations less than 0.1 cm−1 without using any empirically adjustable parameters or optimizing the nuclear mass for a specific transition. For many questionable assignments (deviations > 0.3 cm−1) of observed transitions in H 3 + , a new labeling is proposed. [ABSTRACT FROM AUTHOR]

The projected complex absorbing potential (CAP) technique is one of the methods that allow one to extend the bound state methods for computing resonances' energies and widths. Here, we explore the accuracy of the potential energy curves generated with different electronic structure theory methods in combination with the projected CAP technique by considering resonant vibrational excitation (RVE) of N2 by electron impact as a model process. We report RVE cross sections computed using the boomerang model with potential energy curves obtained with CAP-based extended multistate complete active space perturbation theory (XMS-CASPT2) and equation of motion coupled-cluster method for electron attachment with single and double substitution (EOM-EA-CCSD) methods. We also compare potential energy curves computed with several electronic structure methods, including XMS-CASPT2, EOM-EA-CCSD, multireference configuration interaction with singles (MR-CIS) and singles and doubles (MR-CISD). A good agreement is observed between the experiment and simulated RVE cross sections obtained with the potential energy curves generated with XMS-CASPT2 and EOM-EA-CCSD methods, thus highlighting the potential of the projected CAP technique combined with accurate electronic structure methods for dynamical simulations of the processes that proceed through metastable electronic states. [ABSTRACT FROM AUTHOR]

The projected complex absorbing potential (CAP) technique is one of the methods that allow one to extend the bound state methods for computing resonances' energies and widths. Here, we explore the accuracy of the potential energy curves generated with different electronic structure theory methods in combination with the projected CAP technique by considering resonant vibrational excitation (RVE) of N2 by electron impact as a model process. We report RVE cross sections computed using the boomerang model with potential energy curves obtained with CAP-based extended multistate complete active space perturbation theory (XMS-CASPT2) and equation of motion coupled-cluster method for electron attachment with single and double substitution (EOM-EA-CCSD) methods. We also compare potential energy curves computed with several electronic structure methods, including XMS-CASPT2, EOM-EA-CCSD, multireference configuration interaction with singles (MR-CIS) and singles and doubles (MR-CISD). A good agreement is observed between the experiment and simulated RVE cross sections obtained with the potential energy curves generated with XMS-CASPT2 and EOM-EA-CCSD methods, thus highlighting the potential of the projected CAP technique combined with accurate electronic structure methods for dynamical simulations of the processes that proceed through metastable electronic states. [ABSTRACT FROM AUTHOR]

Our recently published [Weike et al., J. Chem. Phys. 159, 244119 (2023)] spin–orbit coupled diabatic potential energy model for HI is used in a thorough analysis of bound and quasi-bound states as well as elastic and inelastic processes in H + I collisions. The potential energy model, designed explicitly for studying scattering, accurately describes the various couplings in the system, which lead to complex dynamics. Ro-vibronic bound and quasi-bound states related to the adiabatic electronic ground state and an excited electronic state are analyzed. Calculations using the full 104 × 104 diabatic matrix model or a single adiabatic state are compared in order to investigate approximations in the latter. Elastic and inelastic scattering cross sections as well as thermal rates between the ground and first excited fine structure levels of iodine are computed for collision energies up to 12 500 cm−1. Resonances related to the quasi-bound states are analyzed in terms of their energy, width, lifetime, and decay probabilities. The effect of different resonances on the thermal rates is discussed. Resonances between 30 000 and 40 000 cm−1 are also studied for selected values of the total angular momentum, in particular their decay probabilities into different final states of iodine and hence their potential effect on branching ratios in photodissociation of HI. [ABSTRACT FROM AUTHOR]

Optical biosensors with their sensitivity, compact design, and reliability stand out as versatile tools capable of detecting a wide range of analytes. Recently, nanophotonic structures supporting bound states in the continuum (BIC) modes have been actively studied, which is especially interesting for biosensing applications due to their high quality (Q) factor and strongly localized electric field, achieving favorable interaction between field and nanometer scale analyte on the sensing surface. Herein, we demonstrate an optical label-free sensing by accidental or Friedrich–Wintgen (FW) BIC supported on silicon nitride gratings. We compared the sensing performance in terms of bulk, and surface sensitivity, and figure of merit with FW-BIC in the leaky regime and with a symmetry-protected (SP) BIC, which are also supported by the studied platform. We exploit the fact that for FW-BIC a high-Q factor up to 498 comparable to that of SP-BIC (up to 425) retains for a much larger set of interrogation angles, providing excellent interrogation stability. We observed that FW-BIC has slightly higher bulk sensitivity than SP-BIC [186 and 158 nm/RIU (refractive index unit), respectively], but at the same time similar characteristics in terms of surface sensitivity and figure of merit. In addition, we show that both BIC resonances are significantly superior in all respects to the leaky regime due to better field confinement. Finally, the surface of sensing device was also functionalized to detect a cardiac biomarker, myoglobin, exhibiting the limit of detection of 49 ng/ml with clinically relevant level. [ABSTRACT FROM AUTHOR]

Optical eigenstates with a high quality (Q) factor provide substantial advantages for a broad spectrum of optical devices, particularly those demanding strong light–matter interactions. Recently, it has been demonstrated that ultrahigh- Q resonances can be realized in planar photonic structures by merging multiple bound states in the continuum (BICs) in the momentum space. Photonic lattices with thin-film geometry are known to support abundant TE-polarized and TM-polarized BICs. While prior research has explored the merging of TE-polarized BICs, this paper presents analytical and numerical results concerning the merging of TM-polarized BICs in laterally periodic one-dimensional photonic lattices. As the thickness of photonic lattices increases, TM-polarized accidental BICs descend along the dispersion curves and eventually merge at the upper edge of the second stop band. Employing coupled-mode analysis, we calculate the analytical merging thickness at which multiple TM-polarized BICs come together at the second-order Γ point. We confirm the merging of TM-polarized BICs through finite-element method simulations. Our results can be beneficial for achieving ultrahigh- Q resonances through the merging of BICs. [ABSTRACT FROM AUTHOR]

The body–boundary correspondence refers to the relationship between the body and boundary states of topological insulators (TIs). In TIs, the presence of boundary states is connected to the bulk topological properties of the material. The topology can be identified by studying the energy of the topological modes within the bulk bandgap. However, not all topological materials exhibit boundary states within the insulating energy gap. In many cases, the presence of boundary states can be hidden or masked by the bulk energy bands, making it difficult to measure TIs. Recent experiments have shown that defects, which are commonly found in crystalline materials, can be used as probes to explore higher-order topologies that have been recently realized on various platforms. These defects can generate fractional charges and stable bound states in the dispersion region, allowing us to observe the clear body–disclination correspondence. We have performed simulations using a coupled acoustic cavity system with C3 and C5 symmetries to investigate the body–disclination correspondence in topological crystal insulators (TCIs) in the field of acoustics. Simulation and theoretical results have demonstrated that defects such as disclinations can be used to probe higher-order topologies that were previously unobservable in three-dimensional structures. This approach allows us to detect fractional mode charges and stable bound states, which are crucial for understanding the topological nature of TCIs. Our work demonstrates the potential of using disclination defects to study the intricate relationship between the body and boundary states in topological materials, particularly in the context of acoustics. [ABSTRACT FROM AUTHOR]

New six-dimensional ab initio potential energy surfaces (PESs) for the N2–CO2 complex, which involve the stretching vibration of N2 and the Q3 normal mode for the ν3 asymmetric stretching vibration of CO2, were constructed using the CCSD(T)-F12/AVTZ method with midpoint bond functions. Two vibrational averaged 4D interaction potentials were obtained by integrating over the two intramolecular coordinates. It was found that both PESs possess two equivalent T-shaped global minima as well as two in-plane and one out-of-plane saddle points. Based on these PESs, rovibrational bound states and energy levels were calculated applying the radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm. The splitting of the energy levels between oN2–CO2 and pN2–CO2 for the intermolecular vibrational ground state is determined to be only 0.000 09 cm−1 due to the higher barriers. The obtained band origin shift is about +0.471 74 cm−1 in the N2–CO2 infrared spectra with CO2 at the ν3 zone, which coincides with the experimental data of +0.483 74 cm−1. The frequencies of the in-plane geared-bending for N2–CO2 at the ν3 = 0 and 1 states of CO2 turn out to be 21.6152 and 21.4522 cm−1, the latter reproduces the available experimental 21.3793 cm−1 value with CO2 at the ν3 zone. The spectral parameters fitted from the rovibrational energy levels show that this dimer is a near prolate asymmetric rotor. The computed microwave transitions as well as the infrared fundamental and combination bands for the complex agree well with the observed data. [ABSTRACT FROM AUTHOR]

This article presents a method of computing bound state potential curves and autoionizing curves using fixed-nuclei R-matrix data extracted from the Quantemol-N software suite. It is a method based on two related multichannel quantum-defect theory approaches. One is applying bound-state boundary conditions to closed-channel asymptotic solution matrices, and the other is searching for resonance positions via eigenphase shift analysis. We apply the method to the CH molecule to produce dense potential-curve datasets presented as graphs and supplied as tables in the publication supplement. [ABSTRACT FROM AUTHOR]

We have investigated the impact of microsolvation on shape-type resonance states of nucleobases, taking cytosine as a case study. To characterize the resonance position and decay width of the metastable states, we employed the newly developed DLPNO-based EA-EOM-CCSD method in conjunction with the resonance via Padé (RVP) method. Our calculations show that the presence of water molecules causes a redshift in the resonance position and an increase in the lifetime for the three lowest-lying resonance states of cytosine. Furthermore, there are some indications that the lowest resonance state in isolated cytosine may get converted to a bound state in the presence of an aqueous environment. The obtained results are extremely sensitive to the basis set used for the calculations. [ABSTRACT FROM AUTHOR]

Optical chiral metasurfaces with high quality factors enhance light–matter interactions. However, intrinsic chirality based on breaking the symmetry-protected BIC hardly reveals strong circular dichroism (CD) against structural perturbations. Here, we propose a design of the intrinsic chirality empowered by a pair of off-Γ accidental BICs and demonstrate a robust intrinsic chiroptical response continuously exhibiting strong and sign-controllable transmitted CD up to 0.98 and stable high-quality factors under a wide range of perturbations of geometrical parameters. A triangular lattice with slant T-shaped meta-atoms is employed to break all mirror symmetries. The at-Γ quality factor of the chiral resonance is enhanced by four C points and maintains the range of 105–106. Our work is beneficial for designing chiral metasurfaces with a strong intrinsic chirality. [ABSTRACT FROM AUTHOR]

This paper investigates the event‐triggered finite‐time trajectory tracking controller based on a type of chained‐form nonholonomic systems under unknown disturbances by utilizing relay switching technology. A key design idea is that the entire control design is grouped into two separated control stages to produce different finite‐time tracking controllers with correspondingly event‐triggered control rules. By using some nonlinear design methods, a relay switching–based event‐triggered finite‐time tracking control method is adopted to assure that the resulting closed‐loop tracking error system converges to an arbitrarily small neighborhood around zero within a finite time. All closed‐loop error system states keep bounded throughout the entire process. Simulation and experiment results demonstrate the rationality of the designed tracking control strategy. [ABSTRACT FROM AUTHOR]

A normalizable static supersymmetric bound ground state annihilated by the super-generators has got zero number of internal nodes in the framework of one-dimensional supersymmetric quantum mechanics. The super-generator transformations between excited super-partner bound states as combined with the standard technique of Wronskian provide an elegant and self-sufficient way to derive the equality of internal nodes amount to the number of consequent excitations. [ABSTRACT FROM AUTHOR]

The study of band topology in photonic crystals was primarily focused on near-field effects, including edge states and high-order corner states. However, this work investigated the polarization distribution of radiated fields for photonic crystal slabs to get their far-field properties of band topology. We introduced a topological invariant—the winding number of far-field polarization around the Brillouin zone boundary and confirmed a robust correspondence between it and the Chern number of energy bands from the perspective of symmetry, which can be used to analyze the process of topological phase transition. It is found that changes in the winding number and Chern number, associated with the exchange of far-field polarization singularities, especially for bound states in the continuum, will emerge during phase transition. These findings offer insights for further understanding the intriguing properties of topological materials. [ABSTRACT FROM AUTHOR]

To transform bound state‐in‐continuum (BIC)‐related unidirectional radiation into BIC‐related unidirectional lasing, a 1‐D grating with a parity‐time (PT)‐symmetry configuration is proposed. Through non‐Hermitian modulation, the BIC undergoes an asymmetric split in the –k and +k spaces. Abnormal phenomena have also been observed. The asymmetric BIC makes the grating either a gain cavity or a loss cavity depending on the incident direction of the plane wave. With plane wave incidence, the grating exhibits Fano resonance with energy conservation. However, for diverging light incident from a line source or a Gaussian source, the coupling of the gain cavity and loss cavity produces a new phenomenon, unidirectional and single‐mode lasing with an interesting wavefront transformation from a diverging wave to a unidirectional plane wave. The physical mechanism is explained by the joint effect of the asymmetric PT‐BICs and cavity resonance. [ABSTRACT FROM AUTHOR]

We present experimental observations of topological edge states in photonic bilayer Su–Schrieffer–Heeger (SSH) lattices. Using the femtosecond laser direct writing technology, we establish two distinct types of nontrivial bilayer SSH lattices with varying interlayer couplings, allowing us to observe two different types of topological edge states. Interestingly, we find that these topological edge states can either remain within the bandgap or transition into gapless bound states in the continuum without hybridization under different interlayer couplings. Our work illustrates a scheme to investigate topology and bound states in the continuum physics in artificial systems, potentially opening up many possibilities in topology-driven photonic devices. [ABSTRACT FROM AUTHOR]

We investigate how the gravitational field generated by a four-dimensional electrovacuum cosmological space–time influences the dynamics of fermionic fields governed by the Dirac equation, while also considering the effects of topology. We derive the radial wave equation corresponding to the relativistic Dirac equation and obtain analytical solutions for the energy levels and wave functions of the fermionic field within our framework. Our analysis reveals that various parameters, including the cosmological constant, the parameter responsible for space topology, and quantum numbers, play significant roles in determining the eigenvalues of the quantum particles. Specifically, we demonstrate that the presence of the topological parameter disrupts the degeneracy of the energy spectrum. [ABSTRACT FROM AUTHOR]

In this analysis, we investigate hydrogen and pionic atoms subjected to Dirac and Klein-Gordon oscillators, respectively, in the global monopole spacetime. Through a purely analytical analysis, we determine solutions of bound state, in which we define the allowed energy values for the lowest energy state of both proposed systems. In addition to the influence of the topological defect on the results obtained, we note another quantum effect: the oscillation frequencies of both systems depend on the system quantum numbers, that is, the angular frequencies are quantized. [ABSTRACT FROM AUTHOR]

This article proposes the design of the resolution‐dependent variance‐constrained state estimation (RDVCSE) algorithm for a class of time‐varying nonlinear coupled complex networks (TVNCCNs) with stochastic communication and correlated noises. Specifically, a continuous‐differentiable nonlinear function with bounded first partial derivative is considered during the exchange among different coupled units and a resolution‐limited model is taken into account to embody the limited data‐processing capabilities of sensors. In order to describe the principle of random allocation in engineering, a stochastic strategy is employed in the sensor/estimator shared channel. An augmented RDVCSE method is developed such that the error covariance upper bound of state estimation (ECUBSE) can be guaranteed and obtained first. Then, the estimator parameter can be concretized via optimizing the trace of ECUBSE. In addition, a sufficient criterion is provided to verify the uniform boundedness of the presented RDVCSE algorithm. Finally, a comparative simulation is carried out to illustrate the validity of the introduced RDVCSE algorithm. [ABSTRACT FROM AUTHOR]

Topological phases of matter, with their quantized invariants, offer the potential for disorder‐resistant transport via topological bound states. Contrary to the belief that dissipation disrupts Hermiticity and Zak phase quantization, theoretical and experimental evidence of their persistence in a non‐Hermitian photonic waveguide array is presented. A three‐layer Su‐Schrieffer‐Heeger (SSH) chain is demonstrated, which can be split into a Hermitian SSH subspace and a non‐Hermitian ladder subspace through hidden symmetry. This division allows the SSH subspace to retain its topological properties, resulting in a quantized Zak phase and lossless topological bound states. Additionally, the non‐Hermitian subspace supports coherent transport dynamics, with the phase and intensity of bound states fixed at two extreme SSH layers, confirming the presence of the Hermitian subspace. These findings enhance the understanding of the interplay between non‐Hermiticity and topology and pave the way for coherent topological light transport. [ABSTRACT FROM AUTHOR]

While the hydrogen molecular ion is the simplest molecule in nature and very well studied in all of its properties, it remains an interesting system to use for explorations of fundamental questions. One such question treated in this study relates to finding an optimal adiabatic representation of the physics, i.e., the best adiabatic description that minimizes the role of nonadiabatic effects. As a test case explored here in detail, we consider the ungerade symmetry of H 2 + , which is known to have a huge scattering length of order 750 Bohr radii, and an incredibly weakly bound excited state. We show that a hyperspherical adiabatic description does an excellent job of capturing the main physics. Our calculation yields a competitive scattering length and shows that nonadiabatic corrections are small and can even be adequately captured using the post-adiabatic theory of Klar and Fano. [ABSTRACT FROM AUTHOR]

We report an improved variational upper bound for the ground state energy of H− using Hylleraas-like wave functions in the form of a triple basis set having three distinct distance scales. The extended precision DQFUN of Bailey, allowing for 70 decimal digit arithmetic, is implemented to retain sufficient precision. Our result exceeds the previous record [A. M. Frolov, Euro. J. Phys. D 69, 132 (2015)], indicating that the Hylleraas triple basis set exhibits comparable convergence to the widely used pseudorandom all-exponential basis sets, but the numerical stability against roundoff error is much better. It is argued that the three distance scales have a clear physical interpretation. The new variational bound for infinite nuclear mass is –0.527 751 016 544 377 196 590 814 478 a.u. New variational bounds are also presented for the finite mass cases of the hydrogen, deuterium, and tritium negative ions H−, D−, and T−. [ABSTRACT FROM AUTHOR]

In recent years, research on chiral bound states in the continuum (BIC) has surged, leading to the development of various chiral metasurfaces with narrow bandwidths by breaking of in-plane and out-of-plane symmetries. However, the ability to dynamically tune the working band remains relatively unexplored, which is valuable for chiral sensing applications. Optical phase-change materials, with tunable dielectric constants and switchable properties during phase transition, offer the potential for dynamic control of optical metasurfaces. This work demonstrates a wavelength-tunable infrared chiral metasurface by combining the phase-change material GST with chiral BIC structures. By varying the longitudinal tilt angle of the nanostructure, an infrared chiral metasurface with an extremely narrow bandwidth of chiral resonance and a CD value of over 0.8 is designed. The phase-change properties of GST enable wavelength-tunable chiral resonance without altering the structural parameters, and the influence of key structural parameters of the metasurface on the chiral resonance wavelength and CD value is analyzed. The proposed chiral BIC metasurface with phase-change materials shows promising application prospects in filter devices, chiral thermal switches, infrared imaging, and tunable chiral photonics. [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]

Topological insulators and bound states in the continuum represent two fascinating topics in the optical and photonic domain. The exploration of their interconnection and potential applications has emerged as a current research focus. Here, we investigated non-Hermitian photonics based on a parallel cascaded-resonator system, where both direct and indirect coupling between adjacent resonators can be independently manipulated. We observed the emergence of topological Fabry−Pérot bound states in the continuum in this non-Hermitian system, and theoretically validated its robustness. We also observed topological phase transitions and exceptional points in the same system. By elucidating the relationship between topological insulators and bound states in the continuum, this work will enable various applications that harness the advantages of bound states in the continuum, exceptional points, and topology. These applications may include optical delay and storage, highly robust optical devices, high-sensitivity sensing, and chiral mode switching. [ABSTRACT FROM AUTHOR]

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Topology can manifest topological magnetism (e.g., skyrmion and bimeron) in real space and quantum anomalous Hall (QAH) state in momentum space, which has changed the modern conceptions of matter phase. While the topologies in different spaces are widely studied separately, their coexistence and coupling in a single phase are seldom explored. Here, a novel phenomenon is reported that arises from the interaction of topological magnetism and band topology, the multi‐space topology, in 2D ferromagnetic lattice. Based on continuum theory and tight‐binding model, it is revealed that the interconnection between skyrmion/bimeron and QAH state generates distinctive localized chiral bound states (CBSs). With moderating topological magnetism through a magnetic field, the multi‐space topologies accompanied with different CBSs can be reversed, facilitating the coupling of multi‐space topologies. By performing first‐principles and atomic spin model simulations, such multi‐space topologies and their coupling in monolayer Cr2NSb are further demonstrated. These results represent an important step toward the development of multi‐space topological phenomena in 2D lattice. [ABSTRACT FROM AUTHOR]

Metasurfaces have become one of the most prominent research topics in the field of optics owing to their unprecedented properties and novel applications on an ultrathin platform. By combining graphene with metasurfaces, electrical tunable functions can be achieved with fast tuning speed, large modulation depth, and broad tuning range. However, the tuning efficiency of hybrid graphene metasurfaces within the short‐wavelength infrared (SWIR) spectrum is typically low because of the small resonance wavelength shift in this wavelength range. In this work, through the integration of graphene and silicon metasurfaces that support quasi‐bound states in the continuum (quasi‐BIC), the critical coupling as well as transmittance spectrum tuning is experimentally demonstrated. The spectrum tuning is substantial even with less than 30 nm resonance wavelength shift thanks to the high quality factor of quasi‐BIC metasurfaces. The tunable transmittance spectrum is measured using Fourier transform infrared spectroscopy (FTIR) with a modified reflective lens to improve the accuracy, and the electrical tuning is realized utilizing the “cut‐and‐stick” method of ion gel. At the wavelength of 3.0 µm, the measured transmittance change (ΔT  = Tmax  − Tmin) and modulation depth (ΔT/Tmax) can reach 22.2% and 28.9%, respectively, under a small bias voltage ranging from −2 to +2 V. This work demonstrates an effective way of tuning metasurfaces within the SWIR spectrum, which has potential applications in optical modulation, reconfigurable photonic devices, and optical communications. [ABSTRACT FROM AUTHOR]

Optical bound states in the continuum (BICs) lies in side the continuum and coexists with extended waves, but it remains perfectly confined without any radiation. This unique property of BICs has led to numerous applications, such as highly surface‐sensitive and spectrally sharp resonances for photonic biosensors. However, it remains challenging to experimentally realize the BICs in a single‐particle system, especially for subwavelength structures. This study presents the existence of optical BICs in a subwavelength metallic microstructure, and quasi‐BICs are observed experimentally in a waveguide system with only a single optimized aluminum meta‐particle. This plasmonic BICs is resulting from the destructive interference of two localized surface plasmon modes. Benefiting from its strong localized field confinement and substrate‐free merit of BICs, the experimentally measured quality factor (Q‐factor) of this transmission dip reach to 273. Additionally, this meta‐particle is experimentally verified to show a good sensitivity for both solids and liquids through the spectral shift of the BICs caused transmission dip. This finding extends the optical BICs to a subwavelength scale and opens practical application opportunities for ultrasmall‐quantity detection of biochemical substances. [ABSTRACT FROM AUTHOR]

We consider the one-dimensional Schrödinger equation for the sextic anharmonic oscillator potential within the Dunkl formalism. Solutions of bound state type are constructed, and results are compared to the conventional scenario. [ABSTRACT FROM AUTHOR]

Conventional spectrometer designs necessitate a compromise between their resolution and sensitivity, especially as device and detector dimensions are scaled down. Here, we report on a miniaturizable spectrometer platform where light throughput onto the detector is instead enhanced as the resolution is increased. This planar, CMOS-compatible platform is based around metasurface encoders designed to exhibit photonic bound states in the continuum, where operational range can be altered or extended simply through adjusting geometric parameters. This system can enhance photon collection efficiency by up to two orders of magnitude versus conventional designs; we demonstrate this sensitivity advantage through ultralow-intensity fluorescent and astrophotonic spectroscopy. This work represents a step forward for the practical utility of spectrometers, affording a route to integrated, chip-based devices that maintain high resolution and SNR without requiring prohibitively long integration times. [ABSTRACT FROM AUTHOR]

In this issue of Structure , Viennet et al. 1 report a study characterizing the DNA binding by a three-zinc-finger fragment from the transcription factor BCL11A, with the unusual feature that an interfinger interaction in the free protein is disrupted during binding, which provides a positive entropic contribution that enhances the affinity. In this issue of Structure , Viennet et al. report a study characterizing the DNA binding by a three-zinc-finger fragment from the transcription factor BCL11A, with the unusual feature that an interfinger interaction in the free protein is disrupted during binding, which provides a positive entropic contribution that enhances the affinity. [ABSTRACT FROM AUTHOR]

Real‐world resonances face surface‐scaling radiation leakage, hindering light confinement in optically large systems. Conventional bound states in continuum (BICs) challenge this by enabling states with theoretically infinite lifetimes in 2D periodic structures. However, when fabricated, the truncation of these systems to finite sizes inevitably re‐introduces leakage, uncontrollably downgrading their quality factors. Here, a novel form of finite‐size 3D quasi‐BICs (QBICs) is demonstrated that leverage a skyrmion field topology of Bloch modes in 3D cubic photonic crystals. The associated finite systems exhibit highly suppressed radiation in all three spatial directions, with a remarkable exponential volume‐scaling of quality factors. With an unprecedentedly large 3D prototype of 24 cm3 and great scalability, the existence of skyrmion QBICs is experimentally proven through unique far‐field polarization wrapping and spectral singularity. These demonstrations enable to have omnidirectional topological radiation suppression, 3D vortex generation, and access to arbitrarily large volume and volumetric interfaces. 3D QBIC may empower extreme 3D light‐trapping, enhanced volumetric sensing, and topological skyrmion emitters. [ABSTRACT FROM AUTHOR]

Bound states in the continuum are optical modes with extremely high-quality factors and narrow resonances, which exist in the dispersion spectrum of the radiative region above the light line. A unique bound state in the continuum is supported at the edge of truncated photonic crystals, which is a type of a Fabry-Pérot type bound state in the continuum, but has never been observed in experiments. Here, we demonstrate the bound states in the continuum supported at the edge array of silicon (Si) pillars whose diameter is bigger than that of the rest of a Si-pillar two-dimensional photonic crystal. We also show the tunability of the resonance and surface sensitivity of the mode when Si pillars are conformally coated with nanometer-thick aluminium oxide films. The presence of an oxide nanofilm improves the quality factor by over 60 % and shifts the resonance wavelength. Such behavior signifies the substantial potential of the bound states in the continuum on two-dimensional photonic crystals for post-fabrication tuning of the quality factor and surface sensing applications. Optical bound states in the continuum is a highly localized mode supported in various systems. Authors demonstrate such optical modes that propagate at the edge of truncated photonic crystal structures composed of an array of silicon pillars. [ABSTRACT FROM AUTHOR]

Amorphous magnets of the spin-glass type are characterized by completely disordered spatial distribution of magnetic ions, coupled by exchange interaction in such a way that the directions of the spins are also completely random, and the net magnetization is zero. The spin dynamics of such magnets can be described macroscopically by equations for a time-dependent non-uniform is space three-dimensional rotations of the spins. The non-commutative character of such rotations leads to the non-trivial topological properties of the space of dynamical variables, the rotations angles, and to a complex form of the significantly non-linear equations for them. For the disordered magnets of the type of spin glasses, stable three-dimensional topological solitons are found within this phenomenological approach. These solitons are characterized by internal precessional dynamics of the spins, from the quantum-mechanical viewpoint they can be treated as bound states of large number of linear excitations of this system, magnons. [ABSTRACT FROM AUTHOR]

The Aharonov–Bohm effect can be described as a phase difference in interfering charged particles that travel through two distinct pathways oppositely surrounding a perpendicularly-positioned solenoid. The magnetic field emanates from the solenoid but does not intersect the pathways. On the other hand, the Kuramoto model can be used to identify the synchronization conditions that lead to a particular phase difference by treating the phases as coupled oscillators. Starting with the overall wave function expression for the electron in an Aharonov–Bohm potential, we derive a version of the Kuramoto model describing the phase dynamics of the bound state of the quantum mechanical system. We show that the resulting synchronization condition of the model coincides with the allowable values of the flux parameter for our case to achieve an Aharonov–Bohm effect. [ABSTRACT FROM AUTHOR]

We construct approximate bound state solutions to the one-dimensional Schrödinger equation within the Dunkl formalism for a symmetrized Hulthén potential. Our method is based on reducing the governing equation to conventional Schrödinger form, such that an approximation to an inverse quadratic term becomes applicable. Conditions for computing stationary energies, as well as for establishing boundedness and normalizability of our solutions are discussed. [ABSTRACT FROM AUTHOR]

Second‐order topological bound states in the continuum (SOTBICs) have received widely attention in photonics due to theirs counterintuitive localized properties. A model of square‐root SOTBICs is proposed that not only inherit topological features from its parent Hamiltonian, but also support multiple corner states with different propagation constants, a unique feature not found in its parent Hamiltonian. Using femtosecond laser‐writing technology, a photonic nontrivial 2D edge‐centered SSH lattice is fabricated and observe two types of localized corner states with distinct phase distribution. Interestingly, by using an auxiliary waveguide with defined refractive index and coupling into the array, it is experimentally demonstrated that corner states are embedded but do not hybridize with bulk states of the lattice. Additionally, it is experimentally verified that these square‐root SOTBICs are robust against disorders as long as the essential symmetries remain preserved. The work marks the instance of SOTBICs with multiple corner states in photonic lattices. [ABSTRACT FROM AUTHOR]