Related papers: On p-adic Stochastic Dynamics, Supersymmetry and t…
The spreading of a particle along a chain, and its relaxation, are central themes in statistical and quantum mechanics. One wonders what are the consequences of the interplay between coherent and stochastic transitions. This fundamental…
The dynamical symmetry breaking in a quasi-(1+1)-dimensional relativistic model is investigated. The motions of particles in intrachain are described as a relativistic electron-hole gas, while the interchain hopping term is introduced as a…
Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…
A mixed quantal-semiquantal theory is presented in which the semiquantal squeezed-state wave packet describes the heavy degrees of freedom. We first derive mean-field equations of motion from the time-dependent variational principle. Then,…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
We study the effective action describing high-energy scattering processes in the multi-Regge limit of QCD, which should provide the starting point for a new attempt to overcome the limitations of the leading logarithmic and the eikonal…
Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the spectral design. The key is to pair two…
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…
The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations…
Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with an inhomogeneous, anisotropic mass density. The source is modeled as a microlocally isotropic generalized Gaussian random…
We propose a novel mechanism of spontaneous supersymmetry breaking which relies upon an ubiquitous feature of Quantum Field Theory, vacuum condensates. Such condensates play a crucial r\^{o}le in many phenomena. Examples include Unruh…
We present a detailed theory of spectacular semiclassical catastrophes happening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett. {\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems are analyzed.…
The three-dimensional Schr\"odinger equation with a position-dependent (effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum Mechanics. The general solution of SUSY intertwining relations with first order…
We consider the dynamical model of a binary bosonic gas trapped in a symmetric dual-core cigar-shaped potential. The setting is modeled by a system of linearly-coupled one-dimensional Gross-Pitaevskii equations with the cubic self-repulsive…
We study the Caldeira-Leggett model where a quantum Brownian particle interacts with an environment or a bath consisting of a collection of harmonic oscillators in the path integral formalism. Compared to the contours that the paths take in…
This article discusses a p-adic version of the infinite potential well in quantum mechanics (QM). This model describes the confinement of a particle in a p-adic ball. We rigorously solve the Cauchy problem for the Schr\"odinger equation and…
In the present work, we combine the notion of $\mathcal{PT}$-symmetry with that of super-symmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called P{\"o}schl-Teller potential which is…
In this paper we pose two fundamental ideas on the motion of an elementary particle supporting the internal "spin motion" or $\textit{Zitterbewegung}$ and a particle as concentrated energy. First, the particle moves randomly in a limited…
We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy…
A class of above-barrier quantum-scattering problems is shown to provide an experimentally-accessible platform for studying $\mathcal{PT}$-symmetric Schr\"odinger equations that exhibit spontaneous $\mathcal{PT}$ symmetry breaking despite…