Related papers: Classical dynamics on curved Snyder space
The Poincar\'e-Snyder relativity was introduced in an earlier paper of ours as an extended form of Einstein relativity obtained by appropriate limiting setting of the full Quantum Relativity. The latter, with fundamental constants $\hbar$…
The time-dependent Schr\"odinger equation for atomic hydrogen in few-cycle laser pulses is solved numerically. Introducing a positive definite quantum distribution function in energy-position space, a straightforward comparison of the…
The geodesics equations on de Sitter and anti-de Sitter spacetimes of any dimensions, are the starting point for deriving the general form of the Boltzmann equation in terms of conserved quantities. The simple equation for the…
The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of…
We study the quantum theory of the Einstein-Maxwell action with a cosmological term in the spherically symmetric space-time, and explored quantum black hole solutions in Reissner-Nordstrom-de Sitter geometry. We succeeded to obtain analytic…
We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…
We explore the symmetries of classical stationary spacetimes in terms of the dynamics of a spinning string described by a worldsheet supersymmetric action. We show that for stationary configurations of the string, the action reduces to that…
Branching flow -- a phenomenon known for steady wave propagation in two-dimensional weak correlated random potential is also present in the time-dependent Schr\"odinger equation for a single particle in one dimension, moving in a…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
The goal of this article is to investigate the dynamics of semi-relativistic or non-relativistic charged particles in interaction with a scalar meson field. Our main contribution is the derivation of the classical dynamics of a…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions. Our primary focus is on the different timescales involved in the evolution of the observables as they approach statistical…
We present a pedagogical work-in-progress. This textbook aims to introduce Hilbert space representations for quantum and classical dynamics, outlining the mathematical foundations, practical guidance, and Python implementation of dynamical…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically…