Scale invariant distribution functions in quantum systems with few degrees of freedom

TL;DR

This paper introduces a novel form of scale invariance in the distribution functions of quantum observables, which can emerge suddenly after a quantum quench in systems like quantum oscillators, revealing new insights into quantum dynamics.

Contribution

It demonstrates a new type of scale invariance in distribution functions of quantum systems, especially after a quantum quench, with potential applications in matter-wave interferometry.

Findings

Distribution functions diverge logarithmically near classical stable points

Scale invariance can emerge suddenly after a quantum quench

Analysis applies to both linear and nonlinear quantum oscillators

Abstract

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.