The quantum beating and its numerical simulation

TL;DR

This paper investigates how nonlinear interactions in a one-dimensional double well potential suppress quantum beating, providing analytical and numerical insights into the dynamics of initially localized states.

Contribution

It introduces a model with focusing nonlinear point interactions and analyzes the suppression of quantum beating through coupled nonlinear Volterra integral equations.

Findings

Quantum beating is suppressed even for nonlinearity exponents below the critical value.

The study offers analytical and numerical results on state evolution in nonlinear double well potentials.

Complete suppression of beating occurs under certain nonlinear conditions.

Abstract

We examine the suppression of quantum beating in a one dimensional non- linear double well potential, made up of two focusing nonlinear point interactions. The investigation of the Schr\"odinger dynamics is reduced to the study of a system of coupled nonlinear Volterra integral equations. For various values of the geometric and dynamical parameters of the model we give analytical and numerical results on the way states, which are initially confined in one well, evolve. We show that already for a nonlinearity exponent well below the critical value there is complete suppression of the typical beating behavior characterizing the linear quantum case.