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V. P. Berezovoj

Publications and source records attributed to V. P. Berezovoj.

15 recordsLinked to original sources
arXiv2025

Applied Supersymmetry

Supersymmetry is one of the most important and indispensable ingredients of modern theoretical physics. However, the absence, at least at the time of publishing this review, of experimental verification of supersymmetry in elementary particle/high-energy physics casts doubt on the viability of this concept at the energies achievable at the LHC. The more unexpected are either already experimentally verified or proposed for verification manifestations of supersymmetry at the level of low (condensed matter physics, quantum optics) and medium (nuclear physics) energies where standard quantum mechanics works. Using examples of various systems from completely different areas of physics, we discuss the isospectrality of quantum Hamiltonians, hidden and explicit supersymmetry, the advantages of the supersymmetric quantum mechanics approach and its role in quantum engineering.

hep-th↗
arXiv2024

Non-stationary SQM/IST Correspondence and ${\cal CPT}/{\cal PT}$-invariant paired Hamiltonians on the line

We fill some of existed gaps in the correspondence between Supersymmetric Quantum Mechanics and the Inverse Scattering Transform by extending the consideration to the case of paired stationary and non-stationary Hamiltonians. We formulate the corresponding to the case Goursat problem and explicitly construct the kernel of the non-local Inverse Scattering Transform, which solves it. As a result, we find the way of constructing non-hermitian Hamiltonians from the initially hermitian ones, that leads, in the case of real-valued spectra of both potentials, to pairing of ${\cal CPT/PT}$-invariant Hamiltonians. The relevance of our proposal to Quantum Optics and optical waveguides technology, as well as to non-linear dynamics and Black Hole Physics is briefly discussed.

hep-th↗
arXiv2021

Hallmarks of tunneling dynamics with broken reflective symmetry

We study features of tunneling dynamics in an exactly-solvable model of N=4 supersymmetric quantum mechanics with a multi-well potential and with broken reflective symmetry. Quantum systems with a phenomenological potential of this type demonstrate the phenomenon of partial localization of under-barrier states, possibly resulting in the appearance of the so-called "resonant" tunneling, or the phenomenon of coherent tunneling destruction, referring to the complete localization. Taking the partial localization and the coherent tunneling destruction as basic examples, we indicate main advantages of using isospectral exactly-solvable Hamiltonians in studies quantum mechanical systems with two- and three-well potentials. They, in particular, are: having enough freedom of changing the potential shape in a wide range, that allows one to choose an exactly-solvable model close to characteristics of the phenomenological one; ability of changing the number of local minima and symmetry characteristics of the potential (symmetric or deformed) without changing the main part of the spectrum; engaging a smart basis of states, that dramatically decreases the dimensionality of matrices used in the diagonalization procedure of the corresponding spectral problem.

quant-ph↗
arXiv2020

Alternative approaches to the description of quantum dynamics in multi-well potentials

We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the spectral method, which allows to reconstruct the spectrum and stationary functions based on the time-dependent solution of the Schrödinger equation; iii) approximations with exact solutions obtained by the supersymmetric quantum mechanics technique. The latter approach proves to be the most promising as it gives a unique possibility to include the specific multi-well features of the problem directly in the calculation procedure.

quant-ph↗
arXiv2013

Tunneling dynamics in exactly-solvable models with triple-well potentials

Inspired by new trends in atomtronics, cold atoms devices and Bose-Einstein condensate dynamics, we apply a general technique of N=4 extended Supersymmetric Quantum Mechanics to isospectral Hamiltonians with triple-well potentials, i.e. symmetric and asymmetric. Expressions of quantum-mechanical propagators, which take into account all states of the spectrum, are obtained, within the N = 4 SQM approach, in the closed form. For the initial Hamiltonian of a harmonic oscillator, we obtain the explicit expressions of potentials, wavefunctions and propagators. The obtained results are applied to tunneling dynamics of localized states in triple-well potentials and for studying its features. In particular, we observe a Josephson-type tunneling transition of a wave packet, the effect of its partial trapping and a non-monotonic dependence of tunneling dynamics on the shape of a three-well potential. We investigate, among others, the possibility of controlling tunneling transport by changing parameters of the central well, and we briefly discuss potential applications of this aspect to atomtronic devices.

quant-ph↗
arXiv2011

Dynamics of localized states in extended supersymmetric quantum mechanics with multi-well potentials

In this paper we propose a self--consistent approach to the description of temporal dynamics of localized states. This approach is based on exactly solvable quantum mechanical models with multi-well potentials and their propagators. States of Hamiltonians with multi-well potentials form a suitable basis for the expansion of wave packets with different shapes and localization degrees. We also consider properties of the tunneling wave packets, taking into account all states of Hamiltonians with symmetric and asymmetric potentials, as well as their dependence on the degree of localization and deformations of potentials. The study of the dynamics of initially localized states shows that application of the two-state approximation for the description of tunneling is considerably limited, especially for systems, which have several states in the under-barrier region, as for example in modern superconducting quantum interference devices and traps for cold atoms.

hep-th↗
arXiv2010

Multi-well potentials and extended supersymmetric quantum mechanics

Using the formalism of extended $N=4$ supersymmetric quantum mechanics we consider the procedure of the construction of multi--well potentials. We demostrate the form--invariance of Hamiltonians entering the supermultiplet, using the presented relation for integrals, which contain fundamental solutions. The possibility of partial $N=4$ supersymmetry breaking is determined. We also obtain exact forms of multi--well potentials, both symmetric and asymmetric, using the Hamiltonian of harmonic oscillator as initial. The modification of the shape of potentials due to variation of parameters is also discussed, as well as application of the obtained results to the study of tunneling processes.

hep-th↗
arXiv2009

Classical stochastic dynamics and extended $N = 4$ supersymmetric quantum mechanics

This work is aimed at demonstrating the possibility to construct new exactly-solvable stochastic systems by use of the extended supersymmetric quantum mechanics ($N=4 SUSY QM$) formalism. A feature of the proposed approach consists in $N=4 SUSY QM$ the fact that probability densities and so obtained new potentials, which enter the Langevin equation, have a parametric freedom. The latter allows one to change the potentials form without changing the temporal behavior of the dispersion function.

hep-th↗
arXiv2006

Geometrical approach for description of the mixed state in multi-well potentials

We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of different types of dynamics (regular or chaotic) in different wells at the same energy Mixed state reveals unique opportunities in research of quantum manifestations of classical stochasticity. Application of traditional criteria for transition to chaos (resonance overlap criterion, negative curvature criterion and stochastic layer destruction criterion) is inefficient in case of potentials with complex topology. Geometrical approach allows considering only configuration space but not phase space when investigating stability. Trajectories are viewed as geodesics of configuration space equipped with suitable metric. In this approach all information about chaos and regularity consists in potential function. The aim of this work is to determine what details of geometry of potential lead to chaos in Hamiltonian systems using geometrical approach. Numerical calculations are executed for potentials that are relevant with lowest umbilical catastrophes.

nlin.CD↗
arXiv2003

Signatures of Quantum Chaos in Wave Functions Structure for Multi-well 2D Potentials

We propose a new approach to investigation of quantum manifestations of classical stochasticity (QMCS) in wave functions structure, which can be realized in potentials with two and more local minima. The main advantage of the proposed approach is the possibility to detect QMCS in comparison not different wave functions, but different parts of the same wave function. Efficiency of the approach is demonstrated for two potentials: surface quadrupole oscillations (QO) and lower umbillic catastrophe (UC) $D_5$.

nlin.CD↗
arXiv2003

Quantum Manifestations of Classical Stochasticity in the Mixed State

We investigate the QMCS in structure of the eigenfunctions, corresponding to mixed type classical dynamics in smooth potential of the surface quadrupole oscillations of a charged liquid drop. Regions of different regimes of classical motion are strictly separated in the configuration space, allowing direct observation of the correlations between the wave function structure and type of the classical motion by comparison of the parts of the eigenfunction, corresponding to different local minima.

nlin.CD↗
arXiv2001

Quadrupole Oscillations as Paradigm of the Chaotic Motion in Nuclei. Part 2

The present communication is a continuation of the review, the first part of which was presented in nucl-th/0109033. The second part dealswith the manifistation of Chaotic dynamics at quantum level. The variations of statistical properties of energy spectrum in the process of R-C-R transition have been studied in detail. We proved that the type of the classical motion is correlated with the structure of the eigenfunctions of highly excited states in the R-C-R transition. Shell structure destruction induced by the increase of nonintegrable perturbation was analyzed.

nucl-th↗
arXiv2001

Quadrupole Oscillations as Paradigm of the Chaotic Motion in Nuclei. Part 1

We have presented a complete description of classical dynamics generated by the Hamiltonian of quadrupole nuclear oscillations and identified those peculiarities of quantum dynamics that can be interpreted as quantum manifestations of classical stochasticity. Particular attention has been given to investigation of classical dynamics in the potential energy surface with a few local minima. A new technique is suggested for determination of the critical energy of the transition to chaos. It is simpler than criteria of transition to chaos connected with one or another version of overlap resonances criterion. We have numerically demonstrated that for potential with a localized unstable region motion becomes regular at the high energy again, i.e. transition regularity-chaos-regularity {R - C - R} takes place for these potentials. The variations of statistical properties of energy spectrum in the process of {R - C - R) transition have been studied in detail. We proved that the type of the classical motion is correlated with the structure of the eigenfunctions of highly excited states in the (R - C - R) transition. Shell structure destruction induced by the increase of nonintegrable perturbation was analyzed.

nucl-th↗
arXiv2001

Stochastic Resonance in a Periodically Modulated Dissipative Nuclear Dynamics

A fission decay of highly excited periodically driven compound nuclei is considered in the framework of Langevin approach. We have used residual-time distribution (RTD) as the tool for studying of dynamic features in a presence of periodic perturbation. The structure of RTD essentially depends on the relation between Kramers decay rate and the frequency of the periodic perturbation. In particular, intensity of the first peak in RTD has a sharp maximum at certain nuclear temperature depending on the frequency of the periodic perturbation. This maximum should be considered as first-hand manifestation of stochastic resonance in nuclear dynamics.

nlin.CD↗