Computational Studies of Multiple-Particle Nonlinear Dynamics in a Spatio-Temporally periodic potential

TL;DR

This paper investigates the complex nonlinear dynamics of multiple particles in a spatio-temporally periodic potential, highlighting how particle number influences bifurcations and attractors, with implications for experimental analysis of such systems.

Contribution

It introduces a detailed analysis of bifurcations and attractor behavior in multi-particle systems within a STP potential, emphasizing the role of particle number and energy deviations.

Findings

Particle concentration affects bifurcation types and attractor counts.

Odd and even particle numbers lead to different dynamical behaviors.

Energy deviation analysis aids in understanding state transitions.

Abstract

The spatio-temporally periodic (STP) potential is interesting in Physics due to the intimate coupling between its time and spatial components. In this paper we begin with a brief discussion of the dynamical behaviors of a single particle in a STP potential and then examine the dynamics of multiple particles interacting in a STP potential via the electric Coulomb potential. For the multiple particle case, we focus on the occurrence of bifurcations when the amplitude of the STP potential varies. It is found that the particle concentration of the system plays an important role; the type of bifurcations that occur and the number of attractors present in the Poincar\'e sections depend on whether the number of particles in the simulation is even or odd. In addition to the nonlinear dynamical approach we also discuss dependence of the squared fractional deviation of particles kinetic energy of the multiple particle system on the amplitude of the STP potential which can be used to elucidate certain transitions of states; this approach is simple and useful particularly for experimental studies of complicated interacting systems.