Harmonic Potential Research Articles

Integrated optical wave analyzer using the discrete fractional Fourier transform

In this work, we detail a proposal for optical signals to be represented and analyzed in phase-space. Our proposal aims to integrate a series of operations in waveguide realization, as a compact all-together platform that takes an initial wavefield and returns a two-dimensional representation of the information. We show, step by step, that the quantum harmonic oscillator can be considered as a propagator of initial fields, and when a discretized version is implemented, the fractional order Fourier transform emerges. This last is crucial, since the Wigner-Radon theorem is used to establish a path between the propagated wavefield and the phase-space representation. We show by example that this integration offers a direct and efficient method for characterizing optical signals by reconstructing their Wigner phase-space in the scope of integrated optics.

Exploring Ion Polarizabilities and Their Correlation with van der Waals Radii: A Theoretical Investigation.

Polarizability (α) is a fundamental property which measures the tendency of the electron cloud of an atom, ion, or molecule to be distorted by electric field. Polarizability contributes to important physical properties such as molecular interactions or dielectric constants; thus, it is essential to have accurate polarizabilities in molecular simulations. However, it remains a challenge to develop polarizable force fields (FFs) for ions in computational chemistry. In particular, a comprehensive set of polarizabilities for ions has not been derived. Herein, we derived a systematic set of polarizabilities for atoms and ions across the periodic table based on high-level quantum mechanics calculations. These values have excellent agreement with experimental data. Furthermore, we examined the relationship between the obtained polarizabilities and the van der Waals (VDW) radii (RVDW) that we previously determined (J. Chem. Theory Comput., 2023, 19, 2064). Two relationships, RVDW ∝ α1/7 and RVDW ∝ α1/3, proposed in previous studies were examined in the present work. Our results indicated the former relationship, which was derived based on the quantum harmonic oscillator model, prevails for atoms and cations, but neither relationship provides a satisfactory fit for anions. This is consistent with the tight-binding nature of the electrons in atoms and cations, while it is more challenging to quantify the polarizabilities of anions because of their more dispersed electron clouds. Moreover, we compared different approaches to determine the dispersion coefficients, including the London equation, Slater-Kirkwood equation, symmetry-adapted perturbation theory (SAPT) calculations, and time-dependent density functional theory method, along with the approach based on VDW constants. Our results indicated that although different approaches predict deviated magnitudes for the dispersion coefficients, their predictions are highly correlated, implying that each of these approaches can be used to evaluate dispersion interactions after proper scaling. Finally, we have developed a parametrization strategy for the 12-6-4 model based on the obtained insights. We specifically compared the performance of the 12-6-4 model with SAPT and SobEDA analyses to model interactions involving Na+/Mg2+ and various ligands containing He, Ne, Ar, H2O, NH3, [H2PO4]-, and [HPO4]2-. Our results demonstrate that the 12-6-4 parameters effectively reproduce both the total interaction energy and the individual energy components (electrostatics, exchange-repulsion, dispersion, and induction), highlighting the physical robustness of the 12-6-4 model and the effectiveness of our parametrization approach. This study has significant implications for advancing the development of next-generation ion models and polarizable FFs.

Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling

Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling

Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems

Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems

The OU$^2$ process: Characterising dissipative confinement in noisy traps

Abstract The Ornstein-Uhlenbeck (OU) process describes the dynamics of Brownian particles in a confining harmonic potential, thereby constituting the paradigmatic model of overdamped, mean-reverting Langevin dynamics. Despite its widespread applicability, this model falls short when describing physical systems where the confining potential is itself subjected to stochastic fluctuations. However, such stochastic fluctuations generically emerge in numerous situations, including in the context of colloidal manipulation by optical tweezers, leading to inherently out-of-equilibrium trapped dynamics. To explore the consequences of stochasticity at this level, we introduce a natural extension of the OU process, in which the stiffness of the harmonic potential is itself subjected to OU-like fluctuations. We call this model the OU$^2$ process. We examine its statistical, dynamic, and thermodynamic properties through a combination of analytical and numerical methods. Importantly, we show that the probability density for the particle position presents power-law tails, in contrast to the Gaussian decay of the standard OU process. In turn, this causes the trapping behavior, extreme value statistics, first passage statistics, and entropy production of the OU$^2$ process to differ qualitatively from their standard OU counterpart. Due to the wide applicability of the standard OU process and of the proposed OU$^2$ generalisation, our study sheds light on the peculiar properties of stochastic dynamics in random potentials and lays the foundation for the refined analysis of the dynamics and thermodynamics of numerous experimental systems.

Attractive-repulsive interaction in coupled quantum oscillators.

We study the emergent dynamics of quantum self-sustained oscillators induced by the simultaneous presence of attraction and repulsion in the coupling path. We consider quantum Stuart-Landau oscillators under attractive-repulsive coupling and construct the corresponding quantum master equationin the Lindblad form. We discover an interesting symmetry-breaking transition from quantum limit cycle oscillation to a quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from a quantum homogeneous state to an inhomogeneous steady state. The result is supported by the analysis on the noisy classical model of the quantum system in the weak quantum regime. Remarkably, we find the generation of entanglement associated with the symmetry-breaking transition that has no analog in the classical domain. This study enriches our understanding of the collective behaviors shown by coupled oscillators in the quantum domain.

Implementing reactivity in molecular dynamics simulations with harmonic force fields

The simulation of chemical reactions and mechanical properties including failure from atoms to the micrometer scale remains a longstanding challenge in chemistry and materials science. Bottlenecks include computational feasibility, reliability, and cost. We introduce a method for reactive molecular dynamics simulations using a clean replacement of non-reactive classical harmonic bond potentials with reactive, energy-conserving Morse potentials, called the Reactive INTERFACE Force Field (IFF-R). IFF-R is compatible with force fields for organic and inorganic compounds such as IFF, CHARMM, PCFF, OPLS-AA, and AMBER. Bond dissociation is enabled by three interpretable Morse parameters per bond type and zero energy upon disconnect. Use cases for bond breaking in molecules, failure of polymers, carbon nanostructures, proteins, composite materials, and metals are shown. The simulation of bond forming reactions is included via template-based methods. IFF-R maintains the accuracy of the corresponding non-reactive force fields and is about 30 times faster than prior reactive simulation methods.

Classical and quantum analysis of gravitational singularity from Raychaudhuri equation

The present work deals with the Raychaudhuri equation (RE) to examine the space-time singularity both from classical and quantum point of view. The RE has been looked upon in terms of a classical linear Harmonic oscillator and Focusing theorem has been studied. Also, the Raychaudhuri scalar has been shown to affect the convergence and singularity formation in Black-holes and cosmology. Finally, resolution of initial big-bang singularity has been attempted quantum mechanically in two ways namely by canonical quantization and by formulation of Bohmian trajectories.

Dynamics of cosmic string formation with emission of gravitational waves: a toy model

Starting from an extended theory of general relativity with boundary terms included, we study a toy model to describe the dynamical collapse of an infinite cylinder with positive spatial curvature from which a cosmic string is formed after collapsing, and we examine the production of gravitational waves (GW) emitted during the collapse. The background dynamics of the radial collapse is described by a massive scalar field which departs from the equilibrium when the scalar field climbs through the quadratic potential. During the collapse the radial pressure is considered as null, so that the kinetic and the potential energy densities are equaled. The components of the GW modes +,×and B, for the polarization tensor, are analytically obtained.

The explicit bonding reaction ensemble Monte Carlo method.

We present the explicit bonding Reaction ensemble Monte Carlo (eb-RxMC) method, designed to sample reversible bonding reactions in macromolecular systems in thermodynamic equilibrium. Our eb-RxMC method is based on the reaction ensemble method; however, its implementation differs from the latter by the representation of the reaction. In the eb-RxMC implementation, we are adding or deleting bonds between existing particles, instead of inserting or deleting particles with different chemical identities. This new implementation makes the eb-RxMC method suitable for simulating the formation of reversible linkages between macromolecules, which would not be feasible with the original implementation. To enable coupling of our eb-RxMC algorithm with molecular dynamics algorithm for the sampling of the configuration space, we biased the sampling of reactions only within a certain inclusion radius. We validated our algorithm using a set of ideally behaving systems undergoing dimerization and polycondensation reactions, for which analytical results are available. For dimerization reactions with various equilibrium constants and initial compositions, the degree of conversion measured in our simulations perfectly matched the reference values given by the analytical equations. We also showed that this agreement is not affected by the arbitrary choice of the inclusion radius or the stiffness of the harmonic bond potential. Next, we showed that our simulations can correctly match the analytical results for the distribution of the degree of polymerization and end-to-end distance of ideal chains in polycondensation reactions. Altogether, we demonstrated that our eb-RxMC simulations correctly sample both reaction and configuration spaces of these reference systems, opening the door to future simulations of more complex interacting macromolecular systems.

Entanglement in Bound States of Two Particles with a Localized Center-of-Mass Wave-Function

Abstract We explore some entanglement-related features of systems consisting of two particles coupled through a central potential. We consider two types of systems, constituted by particles in one spatial dimension interacting through an attractive Dirac Delta potential, or through a harmonic quadratic potential. The degree of freedom corresponding to the system’s center of mass is either regarded as confined within a one dimensional box, or described by a localized Gaussian wave-packet. As a quantitative indicator of the degree of entanglement between the particles, we use the linear entropy of the one-particle marginal density matrix. In general, this quantity cannot be calculated analytically (except in some special cases related to the Harmonic interaction). Consequently, the linear entropy has to be evaluated numerically. Since the concomitant numerical problem consist in evaluating a multi-dimensional integral in four dimensions, the Monte Carlo integration method is an appropriate one for this task. We explore numerically how the system’s entanglement depends on the different interaction potentials, on the different types of confinement for the system’s center of mass, and on the associated parameters describing the size and geometry of the system.

New slow-roll approximations for inflation in Einstein-Gauss-Bonnet gravity

We propose new slow-roll approximations for inflationary models with the Gauss-Bonnet term. We find more accurate expressions of the standard slow-roll parameters as functions of the scalar field. To check the accuracy of approximations considered we construct inflationary models with quadratic and quartic monomial potentials and the Gauss-Bonnet term. Numerical analysis of these models indicates that the proposed inflationary scenarios do not contradict to the observation data. New slow-roll approximations show that the constructed inflationary models are in agreement with the observation data, whereas one does not get allowed observational parameters at the same values of parameters of the constructed models in the standard slow-roll approximation.

Advanced modeling of higher-order kinematic hardening in strain gradient crystal plasticity based on discrete dislocation dynamics

An extensive study of size effects on the small-scale behavior of crystalline materials is carried out through discrete dislocation dynamics (DDD) simulations, intended to enrich strain gradient crystal plasticity (SGCP) theories. These simulations include cyclic shearing and tension-compression tests on two-dimensional (2D) constrained crystalline plates, with single- and double-slip systems. The results show significant material strengthening and pronounced kinematic hardening effects. DDD modeling allows for a detailed examination of the physical origin of the strengthening. The stress–strain responses show a two-stage behavior, starting with a micro-plasticity regime with a steep hardening slope leading to strengthening, and followed by a well-established hardening stage. The scaling exponent between the apparent (higher-order) yield stress and the geometrical size h varies depending on the test type. Scaling relationships of h−0.2 and h−0.3 are obtained for respectively constrained shearing and constrained tension-compression, aligning with some experimental observations. Notably, the DDD simulations reveal the occurrence of the uncommon type III (KIII) kinematic hardening of Asaro in both single- and double-slip cases, emphasizing the relevance of this hardening type in the realm of small-scale plasticity. Inspired by insights from DDD, two advanced SGCP models incorporating alternative descriptions of higher-order kinematic hardening mechanisms are proposed. The first model uses a Prager-type higher-order kinematic hardening formulation, and the second employs a Chaboche-type (multi-kinematic) formulation. Comparison of these models with DDD simulation results underscores their ability to effectively capture the observed strengthening and hardening effects. The multi-kinematic model, through the use of quadratic and non-quadratic higher-order potentials, shows a notably better qualitative congruence with DDD findings. This represents a significant step towards accurate modeling of small-scale material behaviors. However, it is noted that the proposed models still have limitations, especially in matching the DDD scaling exponents, with both models producing h−1 scaling relationships (i.e., Orowan relationship for precipitate size effects). This indicates the need for further improvements in gradient-enhanced theories in order to guarantee their suitability for practical engineering applications.

Estimating the magnetic field contributions on thermodynamic functions of diatomic molecules trapped in an isotropic oscillator plus inverse quadratic potential

In this study, the Laplace transform approach have been employed to analyze the bound state solutions of two-dimensional Schrödinger equation with isotropic oscillator plus inverse quadratic potential. The wavefunctions and energy equation were derived. Thereafter, the so-called partition function and the thermodynamic properties were evaluated as a function Larmor frequency in the range 0<ωL<100 for some values of parameter λ. The findings showed that both the partition function and thermodynamic properties of the molecules were modified significantly by magnetic interactions, which invariably may alter the macroscopic behaviour of the system examined.

Does the Entropy of Systems with Larger Internal Entanglement Grow Stronger?

It is known that when a system interacts with its environment, the entanglement contained in the system is redistributed since parts of the system entangle with the environment. On the other hand, the entanglement of a system with its environment is closely related to the entropy of the system. However, does this imply that the entropy of systems with larger internal entanglement will grow stronger? We study the issue using the simplest model as an example: system of qubits interacts with the environment described by the quantum harmonic oscillator. The answer to the posed question is ambiguous. However, the study of the situation on average (using the simulation of a set of random states) reveals certain patterns and we can say that the answer is affirmative. At the same time, the choice of states satisfying certain conditions in some cases can change the dependence to the opposite one. Additionally, we show that the entanglement depth also makes a small contribution to entropy growth.

On the shape of the simulated infrared spectral density of strongly hydrogen-bonded systems: Mapping and identification of Hadži ABC structure in phosphonic acid dimers in gas phase

Herein, we explore the origin of three-peaked structure, referred to as the Hadži ABC structure, illustrated within the absorption bands in infrared (IR) spectra of strongly H-bonded systems. The exploration is particularly elucidated for two phosphinic acid dimers (R2POOH) in gas phase, namely bis-(iodomethyl)-phosphinic acid dimer (i.e., R = CH2I) at 465 K and dibutyl-phosphinic acid dimer (i.e., R = C4H9O) at 425 K. A direct theoretical illustration of this spectral signature, related predominantly to very strongly hydrogen bonded complexes, is proposed. The spectral density, υSO−H,is determined by the aid of an approach describing the high-frequency O − H stretching modes by harmonic potentials. The intermolecular potential modes (O…O) are assumed to be of anharmonic nature. The approach is founded on the strong anharmonic coupling approximation, which prescribes a linear dependency of the O − H frequency on the O…O stretching coordinate as rationalized by the fundamental model of Maréchal and Witkowski. Both direct relaxation of the O − H vibrational mode and its homolog, indirect one, affecting the O…O stretching mode are taken into consideration. The model also considers Davydov coupling, which describes the mutual interaction that takes place in the centrosymmetric dimer between the two existent hydrogen bonds as well as Fermi resonances, which occur between the bending modes arising in- and out-of-plane of the dimer and the fundamental O − H stretching mode. Interestingly, we illustrate how the (A, B, and C) triplet detected in the IR absorption band of phosphonic acids can be generated and discuss how the ABC structure can be numerically simulated. The approach provides a direct explanation of the emergence of this unusual feature and mainly reveals that the A peak is due to the Davydov coupling mechanism, whereas the BC diad is found to be generated by Fermi resonances. This was elucidated in a distinctly different approach, rationalized by Sheppard and Claydon, affirming that the provenance of the BC diad is exclusively due to Fermi resonances mechanism. Altogether, our results highlight the congregated effects of both Fermi resonance mechanism and Davydov coupling for the formation of the ABC structure. The model paves the way for a deeper understanding of the ABC structure, characteristic of very toxic strongly hydrogen-bonded dimers. This is of capital importance as it allows one to develop a solid understanding of nerve agents, such as phosphonic acids, from theory alone, so as to avoid difficult and dangerous experiments since they are extremely toxic.

Minimizing the tensor-to-scalar ratio in single-field inflation models

We revisit a class of simple single-field inflation models and demonstrate that they can readily produce a negligible tensor/scalar ratio r. Motivated by recent work suggesting the need to introduce higher order operators to stabilize unregulated potentials, as well as by work indicating that such terms can have significant effects on observable predictions, we explicitly construct corrected versions of the quadratic hilltop potential that are motivated by an effective field theory expansion. We employ Markov Chain Monte Carlo methods and optimization techniques to sample viable models and minimize r. We find that such potentials can readily lower r values below projected CMB-S4 sensitivity, while still remaining within observable constraints on ns. Furthermore, we find that the minimum r reached for each order of the expansion considered is well described by a power law rmin(q)∝q−B before asymptoting to a value of rmin∼10−11, where q is the order to which the expansion of V(ϕ) is carried out. Published by the American Physical Society 2024

Influence of initial correlations on evolution over time of an open quantum system

A novel approach to accounting for the influence of initial system–bath correlations on the dynamics of an open quantum system, based on the conventional projection operator technique, is suggested. To avoid the difficulties of treating the initial correlations, the conventional Nakajima–Zwanzig inhomogeneous generalized master equations (GMEs) for a system’s reduced statistical operator and correlation function are exactly converted into the homogeneous GMEs (HGMEs), which take into account the initial correlations in the kernel governing the evolution of these HGMEs. In the second order (Born) approximation in the system–bath interaction, the obtained HGMEs are local in time and valid at all timescales. They are further specialized for a realistic equilibrium Gibbs initial (at t=t0) system+bath state (for a system reduced statistical operator an external force at t>t0 is applied) and then for a bath of oscillators (Boson field). As an example, the evolution of a selected quantum oscillator (a localized mode) interacting with a Boson field (Fano-like model) is considered at different timescales. It is shown explicitly how the initial correlations influence the oscillator evolution process. In particular, it is shown that the equilibrium system’s correlation function acquires at the large timescale the additional constant phase factor conditioned by survived initial system–bath correlations.

Strongly Rotationally Dependent Lifetimes of C2 in the 23Σg- State: Implications for Predissociation in the Vacuum Ultraviolet Region.

The radiative and photodissociative properties of the dicarbon molecule, C2, in high-lying electronic states are of utmost importance for modeling the photochemical processes that occur in various astronomical environments. Despite extensive spectroscopic studies in the last two centuries, the photodissociation properties of C2 are still largely unknown, particularly for quantum states in the vacuum ultraviolet (VUV) region. Here, the lifetimes of C2 for each individual rovibrational level in the recently identified 23Σg- state are measured for the first time using a VUV-pump-UV-probe photoionization scheme. The lifetimes are found to be strongly dependent on the rotational and vibrational quantum levels in the 23Σg- state. The strongly rotationally dependent lifetimes observed here indicate that the 23Σg- state may mainly undergo a predissociation process through couplings with nearby repulsive electronic states. The current observation could have important applications in modeling the interstellar medium and cometary comae.

Structure and intermolecular interactions in ionic liquid 1-ethyl-3-methylimidazolium bromide and its aqueous solutions investigated by vibrational spectroscopy and quantum chemical computations.

The recently developed efficient protocol to explicit quantum mechanical modeling of structure and IR spectra of liquids and solutions (S. A. Katsyuba, S. Spicher, T. P. Gerasimova, S. Grimme, J. Phys. Chem. B 2020, 124, 6664) is applied to ionic liquid (IL) 1-ethyl-3-methylimidazolium bromide (EmimBr), its C2-deuterated analog [Emim-d]Br and its aqueous solutions. It is shown that the solvation strongly modifies frequencies and IR intensities of the CH/CD stretching vibrations (νCH/νCD) of the imidazolium ring. The main vibrational spectroscopic features of the neat IL are reproduced by the simulations for a cluster (EmimBr)9, in which all three imidazolium CH moieties of the solvated cation form short contacts with three Br- anions, and another two Br- anions are located on top and bottom of imidazolium ring. Cluster models of aqueous solutions reproduce the experimental vibrational frequencies of actual solutions, provided that the Br- anion of solvated contact ion pair (CIP) is situated on top of imidazolium ring, and CH/CD moieties of the latter participate in short contacts with surrounding water molecules. Both structural and spectroscopic analysis allow to interpret the short contacts CH/CD⋯Br- and CH/CD⋯OH2 as hydrogen bonds of approximately equal strength. Enthalpies of bonding of these liquid-state H-bonds, estimated with the use of empirical correlations, amount to ca. 1.4 kcal⋅mol-1, while the analogous estimates obtained for the gas-phase charged species [Emim]2Br+ increase to 5.6 kcal⋅mol-1. It is shown that formation of solvent-shared ion pair (SIP) in aqueous solution, where the counterions of IL are separated by two water molecules H-bonded to a Br- anion, produces frequency shifts ΔνCH/CD, strongly different from the case of CIP formation. This difference can be used for IR/Raman spectroscopic differentiation of the type of solvated ion pairs of EmimBr or other related ILs.