Diffractive energy spreading and its semiclassical limit

TL;DR

This paper investigates how driven quantum systems with energy jumps relate to their classical counterparts, revealing complex quantum-classical transition behaviors through a model analogy with Bloch electrons.

Contribution

It introduces a novel perspective by mapping energy space dynamics of driven systems to a tight-binding model of Bloch electrons, elucidating the quantum-classical correspondence.

Findings

Energy space dynamics resemble Bloch electron models

Long-range hopping influences energy spreading

Quantum-classical transition is highly non-trivial

Abstract

We consider driven systems where the driving induces jumps in energy space: (1) particles pulsed by a step potential; (2) particles in a box with a moving wall; (3) particles in a ring driven by an electro-motive-force. In all these cases the route towards quantum-classical correspondence is highly non-trivial. Some insight is gained by observing that the dynamics in energy space, where $n$ is the level index, is essentially the same as that of Bloch electrons in a tight binding model, where $n$ is the site index. The mean level spacing is like a constant electric field and the driving induces long range hopping 1/(n-m).