Symmetric Potential Research Articles

Information in feedback ratchets.

Feedback control uses the state information of the system to actuate on it. The information used implies an effective entropy reduction of the controlled system, potentially increasing its performance. How to compute this entropy reduction has been formally shown for a general system and has been explicitly computed for spatially discrete systems. Here, we address a relevant example of how to compute the entropy reduction by information in a spatially continuous feedback-controlled system. Specifically, we consider a feedback flashing ratchet, which constitutes a paradigmatic example for the role of information and feedback in the dynamics and thermodynamics of transport induced by the rectification of Brownian motion. A Brownian particle moves in a periodic potential that is switched on and off by a controller. The controller measures the position of the particle at regular intervals and performs the switching depending on the result of the measurement. This system reaches a long-time dynamical regime with a nonzero mean particle velocity, even for a symmetric potential. Here, we calculate the efficiency at maximum power in this long-time regime, computing all the required contributions. We show how the entropy reduction can be evaluated from the entropy of the non-Markovian sequence of control actions, and we also discuss the required sampling effort for its accurate computation. Moreover, the output power developed by the particle against an external force is investigated, which-for some values of the system parameters-is shown to become larger than the input power provided by the switching of the potential. The apparent efficiency of the ratchet thus becomes higher than one, if the entropy reduction contribution is not considered. This result highlights the relevance of including the entropy reduction by information in the thermodynamic balance of feedback-controlled devices, specifically when writing the second principle. The inclusion of the entropy reduction by information leads to a well-behaved efficiency over all the range of parameters investigated.

Self-defocusing nonlinear coupled system with PT-symmetric super-Gaussian potential.

The stationary solutions of the coupled nonlinear Schrödinger equation with self-defocusing nonlinearity and super-Gaussian form of parity-time (PT) symmetric potential in an optical system have been analyzed. The stationary eigenmodes of the ground and excited states and the influence of the gain/loss coefficient on the eigenvalue spectra are discussed. The threshold condition of the PT-symmetric phase transition of the high and low-frequency modes has been studied. Also, the variation of the threshold values with the coupling constant and the effect of the nonlinearity on the eigenmodes are analyzed. The stability of the solution is verified using the linear-stability analysis. In addition, the power distribution of the fundamental solutions with the propagation, in the two channels of the system, is analyzed in the PT and broken PT regimes.

Deep learning neural network for approaching Schrödinger problems with arbitrary two-dimensional confinement

This article presents an approach to the two-dimensional Schrödinger equation based on automatic learning methods with neural networks. It is intended to determine the ground state of a particle confined in any two-dimensional potential, starting from the knowledge of the solutions to a large number of arbitrary sample problems. A network architecture with two hidden layers is proposed to predict the wave function and energy of the ground state. Several accuracy indicators are proposed for validating the estimates provided by the neural network. The testing of the trained network is done by applying it to a large set of confinement potentials different from those used in the learning process. Some particular cases with symmetrical potentials are solved as concrete examples, and a good network prediction accuracy is found.

Tunneling times of an electron in one-dimensional symmetric and asymmetric harmonic double-well potentials

Tunneling times of an electron in one-dimensional symmetric and asymmetric harmonic double-well potentials

Wigner time delay in photoionization: a 1D model study

In scattering theory, the Wigner–Smith time delay, calculated through a phaseshift derivative or its multichannel generalization, has been demonstrated to measure the amount of delay or advance experienced by colliding particles during their interaction with the scattering potential. Fetic, Becker, and Milosevic argue that this concept cannot be extended to include photoionization, viewed as a half-scattering experiment. Their argument is based on the lack of information about scattering phaseshifts in the part of the wavefunction (satisfying the ingoing-wave boundary condition) going to the detector. This article aims to test this claim by examining a photodetachment process in a simple 1D model with a short-range symmetrical potential. Using time-dependent perturbation theory with a dipole interaction, the relevant wavepacket of the outgoing particle is analyzed and compared to the free wavepacket as a reference. Our findings confirm that, indeed, a time delay arises in the liberated fragmentation wavepacket, which is expressed as an energy derivative of the scattering phaseshift. Our study highlights that the source of the phaseshift content in the wavepacket arriving at the detector is the dipole matrix element, which is a direct consequence of imposing the ingoing-wave boundary condition. We illustrate our results through numerical simulations of both the non-free and free wavepackets. The amount of the observed time delay is found to be half of that appearing in a typical scattering experiment.

Exactly solvable complex PT symmetry potential A[sech(λx) + i tanh(λx)

We obtained the exact solutions of the PT symmetric potential V(x) = A[sech(λx) + i tanh(λx)] and found that this system has no bound-state. The PT symmetric potential was first studied in this article, and the handedness effect is shown from reflection coefficients. As the asymptotically non-vanishing imaginary potential component, when the direction of the incident wave is opposite, the transmission coefficient will emerge a complex phase factor.

Spectrum of a q$$ q $$‐deformed Schrödinger equation by means of the variational method

In this work, the ‐deformed Schrödinger equations defined in different form of the ‐Hamiltonian for ‐harmonic oscillator are considered with symmetric, asymmetric, and non‐polynomial potentials. The spectrum of the ‐Hamiltonian is obtained by using the Rayleigh‐Ritz variational method in which the discrete ‐Hermite I polynomials are taken as the basis. As applications, ‐harmonic, purely ‐quartic, and ‐quartic oscillators are examined in the class of symmetric polynomial potentials. Moreover, the ‐version of Gaussian potential for an example of a non‐polynomial symmetric potential and a specific example of ‐version of asymmetric double well potential are presented. Numerous results are given for these potentials for several values of . The limit relation as is discussed. The obtained results of ground‐ and excited‐state energies of the purely ‐quartic oscillator and the accuracy of the ground‐state energy levels are compared with the existing results. Also, the results are compared with the classical case appearing in the literature in the limiting case .

Amplitude-phase modulated composite waves in coupled nonlocal system with self-induced PT symmetric potential.

We consider a coupled nonlocal nonlinear Schrödinger equation (nNLSE) with self-induced parity-time (PT) symmetric potential and investigate abundant amplitude-phase modulated composite waves manifesting diverse evolution patterns. It is found that the coupled nonlocal model can be decoupled into nNLSEs with self-induced PT symmetric potential under certain constraints through a general linear transformation with amplitude and phase modulation. Based on the exact solutions of the nNLSEs with self-induced PT potential, we study various composite waves superposed by bright and/or dark soliton solutions, rogue waves, bright/dark soliton and periodic soliton, and present the abundant evolution patterns under amplitude-phase modulation. The results here only demonstrate the characteristics of limited superposed composite waves. In fact, there exist infinite possible evolution patterns of composite waves due to the arbitrary amplitude-phase modulation in coupled nonlocal nonlinear system with self-induced PT symmetric potential.

Complex S3-symmetric 3HDM

CP violation plays a very important role in nature with implications both for Particle Physics and for Cosmology. Accounting for the observed matter-antimatter asymmetry of the Universe requires the existence of new sources of CP violation beyond the Standard Model. In models with an extended scalar sector CP violation can emerge either explicitly, i.e., at the Lagrangian level, or spontaneously. Spontaneous CP violation occurs in the framework of the electroweak symmetry breaking whenever the Lagrangian conserves CP and the vacuum breaks it. This requires that not all vacuum expectation values be real. In the context of multi-Higgs extensions of the Standard Model imposing the existence of a scalar basis where all couplings are real is a sufficient condition for CP to be explicitly conserved. We discuss a three-Higgs-doublet model with an underlying S3 symmetry, allowing in principle for complex couplings. In this framework it is possible to have either spontaneous or explicit CP violation in the scalar sector, depending on the regions of parameter space corresponding to the different possible vacua of the S3 symmetric potential. We list all possible vacuum structures allowing for CP violation in the scalar sector specifying whether it can be explicit or spontaneous. It is by now established that CP is violated in the flavour sector and that the Cabibbo-Kobayashi-Maskawa matrix is complex. In order to understand what are the possible sources of CP violation in the Yukawa sector we analyse the implications of the different available choices of representations for the quarks under the S3 group. This classification is based strictly on the exact S3-symmetric scalar potential with no soft symmetry breaking terms. The scalar sector of one such model was explored numerically. After applying the theoretical and the most important experimental constraints the available parameter space is shown to be able to give rise to light neutral scalars at the mathcal{O} (MeV) scale.

Point symmetries of the Lie of the complex Ginzburg-Landau equation

A soliton is a nonlinear single moving wave that retains its shape and velocity during its movement, that is, it is a constant formation, and when it collides with isolated waves similar to itself, the phenomenon of a mutual phase shift of two waves occurs, that is, the only result of the interaction of solitons may be some kind of shift in phase. In this paper, we will study the distribution of the soliton constant in the complex Ginzburg-Landau equation (CGL) with a nonlinear regime that focuses on itself in the presence of a symmetric Gaussian potential. For many decades, nonlinear systems have attracted researchers theoretically and experimentally with their rich dynamic characteristics. Such nonlinear systems can be conservative (closed) or dissipative (open), and both support solitons. A soliton is nothing but a constant profile of light pulses in an optical system. In the case of a dissipative nonlinear system, in addition to dispersion and nonlinear equilibrium, it is possible to continuously propagate a light pulse or soliton to achieve a balance between dissipation (loss) and gain. This means that a dissipative system cannot support continuous families of solitons similar to conservative systems. In other words, in a dissipative system, the distribution of solitons can be determined by the parameters of the system, while in a conservative system it is determined by the input optical pulse. This increases the experimental feasibility of determining the area of a stable soliton in a dissipative system by simply manipulating the system.

A completely solvable new $$\mathcal{{PT}}$$-symmetric periodic potential with real energies

A completely solvable new $$\mathcal{{PT}}$$-symmetric periodic potential with real energies

The Dirac equation with /non--symmetric potentials in curved spacetime backgrounds

In this paper, we have presented the Dirac equation in the frame of position-dependent mass on two dimensional gravitational static background in the presence of /non--symmetric potential interactions. The exponential metric component have formed the reduced Dirac operator into the general supersymmetric model within mass changing with coordinates. We have obtained the eigenvalues of the Dirac operator for the complex Morse and trigonometric complex Scarf-II potentials SL(2, C) using Lie algebras and the supersymmetric quantum mechanical approaches. Moreover, after obtaining a general Sturm-Liouville type equation using a convenient mapping, the system have become available to be investigated within η- pseudo-Hermiticity. With this context, η operator is found for the examples of complex trigonometric Rosen-Morse potential and complex Morse potentials with real and complex parameters of the initial system and finally the solutions are obtained for each model with the graphics of energy values and probability densities.

Temperature anomalies of oscillating diffusion in ac-driven periodic systems.

We analyze the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low-friction regime in which the diffusion coefficient shows giant damped quasiperiodic oscillations as a function of the amplitude of the time-periodic force [I. G. Marchenko et al., Chaos 32, 113106 (2022)1054-150010.1063/5.0117902]. We find out that when temperature grows the diffusion coefficient increases at its minima; however, it decreases at the maxima within a finite temperature window. This curious behavior is explained in terms of the deterministic dynamics perturbed by thermal fluctuations and mean residence time of the particle in the locked and running trajectories. We demonstrate that temperature dependence of the diffusion coefficient can be accurately reconstructed from the stationary probability to occupy the running trajectories.

Casimir energy for spinor fields with δ-shell potentials

This work analyzes the Casimir energy of a massive spinor field propagating in flat space endowed with a spherically symmetric δ-function potential. By utilizing the spectral zeta function regularization method, the Casimir energy is evaluated after performing a suitable analytic continuation. Explicit numerical results are provided for specific cases in which the Casimir energy is unambiguously defined. The results described in this work represent a generalization of the MIT bag model for spinor fields.

Paradoxical nature of negative mobility in the weak dissipation regime.

We reinvestigate a paradigmatic model of nonequilibrium statistical physics consisting of an inertial Brownian particle in a symmetric periodic potential subjected to both a time-periodic force and a static bias. In doing so, we focus on the negative mobility phenomenon in which the average velocity of the particle is opposite to the constant force acting on it. Surprisingly, we find that in the weak dissipation regime, thermal fluctuations induce negative mobility much more frequently than it happens if dissipation is stronger. In particular, for the very first time, we report a parameter set in which thermal noise causes this effect in the nonlinear response regime. Moreover, we show that the coexistence of deterministic negative mobility and chaos is routinely encountered when approaching the overdamped limit in which chaos does not emerge rather than near the Hamiltonian regime of which chaos is one of the hallmarks. On the other hand, at non-zero temperature, the negative mobility in the weak dissipation regime is typically affected by weak ergodicity breaking. Our findings can be corroborated experimentally in a multitude of physical realizations, including, e.g., Josephson junctions and cold atoms dwelling in optical lattices.

Physics-informed Neural Network method for predicting soliton dynamics supported by complex PT-symmetric potentials

Abstract We examine the deep learning technique referred to as the physics-informed neural network method for approximating non-linear Schrödinger equation under considered parity time symmetric potentials and obtaining multifarious soliton solutions. For the first time, neural networks founded principally physical information are adopted to figure out the solution the examined non-linear partial differential equation and generate six different types of soliton solutions, which are basic, dipole, tripole, quadruple, pentapole and sextupole solitons we consider. We make comparisons between the predicted and actual soliton solutions to see whether deep learning is capable of seeking the solution the partial differential equation described before. We may assess whether physics-informed neural network is capable of effectively providing approximate soliton solutions through the evaluation of squared error between the predicted and numerical results. Besides, we also scrutinize how different activation mechanisms and network architectures impact the capability of selected deep learning technique works. Through the findings we can prove that the neural networks model we established can be utilized to accurately and effectively approximate non-linear Schrödinger equation under consideration and predict the dynamics of soliton solution.

Physics-Informed Neural Network Method for Predicting Soliton Dynamics Supported by Complex Parity-Time Symmetric Potentials

We examine the deep learning technique referred to as the physics-informed neural network method for approximating the nonlinear Schrödinger equation under considered parity-time symmetric potentials and for obtaining multifarious soliton solutions. Neural networks to found principally physical information are adopted to figure out the solution to the examined nonlinear partial differential equation and to generate six different types of soliton solutions, which are basic, dipole, tripole, quadruple, pentapole, and sextupole solitons we consider. We make comparisons between the predicted and actual soliton solutions to see whether deep learning is capable of seeking the solution to the partial differential equation described before. We may assess whether physics-informed neural network is capable of effectively providing approximate soliton solutions through the evaluation of squared error between the predicted and numerical results. Moreover, we scrutinize how different activation mechanisms and network architectures impact the capability of selected deep learning technique works. Through the findings we can prove that the neural networks model we established can be utilized to accurately and effectively approximate the nonlinear Schrödinger equation under consideration and to predict the dynamics of soliton solution.

Relativistic ratcheting on the surface of topological insulator Bi2Se3 attached to spiral multiferroic oxide

Relativistic ratcheting of Dirac fermions on the surface of topological insulator Bi2Se3 attached to a spiral multiferroic oxide is investigated. We find that the Dirac fermions on the surface of topological insulator Bi2Se3 exhibit pronounced Brownian motion, tuned by the strength of exchange field established by the interaction of spin degrees of Dirac fermions and multiferroic oxide. The surface Dirac fermions show ratchet effect as a net current under the influence of orthogonal, commensurate ac drives in the presence of a symmetric periodic potential set by the exchange field.

Making sense of transmission resonances and Smith lifetimes in one-dimensional scattering: The extended phase space quantum trajectory picture

Resonances are ubiquitous in a wide range of physical and chemical phenomena. Their impact on quantum scattering processes renders their study as important as it can be puzzling. In this paper, we illustrate the accuracy of a fully quantum, purely trajectory based reformulation of quantum mechanics proposed by one of the authors (Poirier) to acquire insights on shape resonances through direct and accurate computation of the diagonal elements of Smith’s lifetime matrix. This study also generalizes the relationship between the quantum trajectory propagation time and the Eisenbud–Wigner time delay – introduced in our previous publication (Dupuy et al., 2022) for symmetric potentials – to the general case of asymmetric potential profiles. In addition, we show how the complex amplitudes of the scattering matrix can be extracted from left- and right-incident quantum trajectories. Finally, we demonstrate that extended phase space quantum trajectories not only recover S-matrix and quantum time quantities, but they also provide their own picture of resonant phenomena, as dynamically distinct events characterized by an integer number of closed orbits in the quantum phase space.

Integrability and exact solutions for a nonlocal matrix nonlinear Schrödinger equation with self-induced $$\mathcal{P}\mathcal{T}$$-symmetric potentials

Integrability and exact solutions for a nonlocal matrix nonlinear Schrödinger equation with self-induced $$\mathcal{P}\mathcal{T}$$-symmetric potentials