Quantum Diffusion Induced by Small Quantum Chaos

TL;DR

This paper demonstrates that quantum systems with classical chaos can induce global quantum diffusion, especially when coupled with additional degrees of freedom, revealing a quantum transition to diffusion through a critical sub-diffusion phase.

Contribution

It introduces a model of small quantum chaos coupled with extra modes, showing how quantum diffusion emerges and transitions occur as coupling strength varies.

Findings

Diffusion occurs in additional modes with increasing coupling strength.

A quantum transition to diffusion happens at a critical point for large N.

Sub-diffusion characterized by an anomalous exponent is observed.

Abstract

It is demonstrated that quantum systems classically exhibiting strong and homogeneous chaos in a bounded region of the phase space can induce a global quantum diffusion. As an ideal model system, a small quantum chaos with finite Hilbert space dimension $N$ weakly coupled with $M$ additional degrees of freedom which is approximated by linear systems is proposed. By twinning the system, the diffusion process in the additional modes can be numerically investigated without taking the unbounded diffusion space into account explicitly. Even though $N$ is not very large, diffusion occurs in the additional modes as the coupling strength increases if $M \geq 3$. If $N$ is large enough, a definite quantum transition to diffusion takes place through a critical sub-diffusion characterized by an anomalous diffusion exponent.