Related papers: Quantum and classical solutions for free particle …
We discuss a class of quantum Abraham models in which the N-particle spinor wave function of N electrons solves a Pauli respectively Schroedinger equation, featuring regularized classical electromagnetic potentials which solve the…
The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hidden $\text{SU}(2) \times \text{SU}(2)$ symmetry, we discuss…
Particles traveling in aligned crystals at small angles w.r.t. crystallographic axes or planes are principally steered by the continuous Lindhard potential. This interaction conserves the energy E, the longitudinal momentum p_parallel, the…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution.…
The paper contains description of the path integrals in the action-angle phase space. It allows to split the action and angle degrees of freedom and to show that the angular quantum corrections cancel each other if the classical classical…
Gravitational D-dimensional model with l scalar fields and several forms is considered. When cosmological type diagonal metric is chosen, an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are…
We consider the free motion of a point particle inside a circular billiard with periodically moving boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the energy of the particle is not…
We illustrate some of the techniques to identify chaos signatures at the quantum level using as a guiding examples some systems where a particle is constrained to move on a radial symmetric, but non planar, surface. In particular, two…
In this article we study the dynamics of one-dimensional relativistic billiards containing particles with positive and negative energy. We study configurations with two identical positive masses and symmetric positions with two massless…
We show that the bounded solutions to the fractional Helmholtz equation, $(-\Delta)^s u= u$ for $0<s<1$ in $\mathbb{R}^n$, are given by the bounded solutions to the classical Helmholtz equation $(-\Delta)u= u$ in $\mathbb{R}^n$ for $n \ge…
Cosmological billiards arise as a map of the solution of the Einstein equations, when the most general symmetry for the metric tensor is hypothesized, and points are considered as spatially decoupled in the asymptotic limit towards the…
We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is $S/\hbar = \int…
The dynamics of three soft interacting particles on a ring is shown to correspond to the motion of one particle inside a soft triangular billiard. The dynamics inside the soft billiard depends only on the {\it masses ratio} between…
Elementary particles are found in two different situations: (i) bound to metastable states of matter, for which angular momentum is quantized, and (ii) free, for which, due to their high energy-momentum and leaving aside inner a.m. or spin,…
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or…
The quantum mechanical version of a classical model for studying the orientational degrees of freedom corresponding to a nematic liquid composed of biaxial molecules is presented. The effective degrees of freedom are described by operators…
Using a quantum fluid model, a set of three paraxial coupled equations to describe the FEL instability is derived. These equations are solved numerically considering Laguerre-Gaussian modes as the initial conditions to study the transfer of…
We study the quantum backflow problem in the noncommutative plane. In particular, we have considered a charged particle with and without an oscillator interaction with noncommuting momentum operators and examined angular momentum backflow…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…