Symmetry-Induced Logarithmic Relaxation in the Quantum Kicked Rotor

TL;DR

This paper investigates how discrete symmetries in the quantum kicked rotor lead to glass-like slow logarithmic relaxation, revealing a novel connection between quantum coherence and slow dynamics.

Contribution

It demonstrates that a discrete mirror symmetry causes quasi-degenerate Floquet doublets and results in logarithmic relaxation in a quantum system, a phenomenon not previously observed in this context.

Findings

Formation of Floquet doublets localized at opposite momenta

Exponential hierarchy of dynamical timescales

Observation of slow logarithmic relaxation behavior

Abstract

We study the effect of discrete symmetries on coherent multiple scattering in the quantum kicked rotor. When the initial momentum is set to zero -- as in recent Bose-Einstein condensate experiments -- the effective pseudo-disorder becomes even under momentum inversion. The resulting discrete mirror symmetry of the dynamics profoundly alters spectral correlations: it generates quasi-degenerate Floquet doublets localised at opposite momenta, whose exponentially small splittings produce a hierarchy of exponentially large dynamical timescales. The coherent backscattering and forward-scattering peaks then exhibit a striking non-monotonic evolution and strongly asymmetric contrasts, followed by an exceptionally slow logarithmic relaxation toward a common asymptotic value -- a hallmark of glassy dynamics, here emerging in a fully coherent quantum system. That such archetypal glass-like behaviour arises from a single discrete symmetry constraint reveals an unexpected and deep connection between quantum coherence and slow relaxation phenomena.