Super revivals and sub-Planck scale structures of a slightly relativistic particle in a box

TL;DR

This paper investigates how tiny relativistic effects dramatically alter the quantum revival dynamics and sub-Planck structures of a particle in a box, revealing a new time scale and enhanced sensitivity to relativistic corrections.

Contribution

It introduces a novel time scale for revivals caused by relativistic corrections and analyzes the impact on sub-Planck structures in a particle in a box.

Findings

Discovery of a new, longer revival time scale due to relativistic effects

Enhanced sensitivity of sub-Planck structures to relativistic corrections

Manifestation of perfect revivals at the new time scale

Abstract

The time evolution of a particle, caught in an infinitely deep square well, displays unexpected features, when one includes tiny relativistic effects. Indeed, even the smallest corrections to the non-relativistic quadratic spectrum manifest themselves in a dramatic way. Our theoretical analysis brings to light a completely new time scale, at which the system exhibits surprisingly perfect revivals. This longer time scale rules the system dynamics and replaces the original revival time of the unperturbed system. The early manifestation of such phenomenon is captured by the sensitivity of sub-Planck structures for different values of the relativistic corrections.