Semilinear response for the heating rate of cold atoms in vibrating traps

TL;DR

This paper develops a semilinear response theory for calculating the heating rate of cold atoms in vibrating traps, especially when traditional linear response assumptions fail due to system-specific matrix textures and sparsity.

Contribution

It introduces an improved sparse random matrix model that captures the effects of geometry-induced texture and sparsity, leading to a generalized variable range hopping framework.

Findings

The texture and sparsity of the perturbation matrix significantly influence heating rates.

A new sparse random matrix model effectively describes the system's response.

The approach extends beyond traditional linear response, accommodating non-chaotic regimes.

Abstract

The calculation of the heating rate of cold atoms in vibrating traps requires a theory that goes beyond the Kubo linear response formulation. If a strong "quantum chaos" assumption does not hold, the analysis of transitions shows similarities with a percolation problem in energy space. We show how the texture and the sparsity of the perturbation matrix, as determined by the geometry of the system, dictate the result. An improved sparse random matrix model is introduced: it captures the essential ingredients of the problem, and leads to a generalized variable range hopping picture.