Quantum anomalies and linear response theory

TL;DR

This paper investigates how quantum anomalies affect energy diffusion in chaotic driven systems, revealing a universal paradigm and nonlinear effects absent in classical approximations.

Contribution

It introduces a new understanding of quantum anomalies in energy diffusion, highlighting the role of a generalized Wigner time and intrinsic dephasing.

Findings

Quantum anomalies lead to nonlinear energy diffusion dependence.

A universal paradigm for diffusive energy spreading in quantum chaotic systems.

Identification of a generalized Wigner time as a key parameter.

Abstract

The analysis of diffusive energy spreading in quantized chaotic driven systems, leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient $D$ that is proportional to the intensity $\epsilon^2$ of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time $t_{\epsilon}$, and a self-generated (intrinsic) dephasing process leads to non-linear dependence of $D$ on $\epsilon^2$.