Enhancement in Breaking of Time-reversal Invariance in the Quantum Kicked Rotor

TL;DR

This paper investigates how a magnetic field influences the breaking of time-reversal symmetry in the quantum kicked rotor, revealing a transition that depends on system parameters and deviates from random matrix theory predictions.

Contribution

It demonstrates the dependence of the TRI to TRNI transition on the ratio of chaos parameter squared to matrix dimension, highlighting deviations from random matrix theory.

Findings

Transition depends on $rac{ ext{chaos parameter}^2}{N}$

Deviation from random matrix theory occurs when $rac{ ext{chaos parameter}^2}{N} < N$

Transition speed increases as $rac{ ext{chaos parameter}^2}{N}$ decreases

Abstract

We study the breaking of time-reversal invariance (TRI) by the application of a magnetic field in the quantum kicked rotor (QKR), using Izrailev's finite-dimensional model. There is a continuous crossover from TRI to time-reversal non-invariance (TRNI) in the spectral and eigenvector fluctuations of the QKR. We show that the properties of this TRI $\rightarrow$ TRNI transition depend on $\alpha^2/N$, where $\alpha$ is the chaos parameter of the QKR and $N$ is the dimensionality of the evolution operator matrix. For $\alpha^2/N \gtrsim N$, the transition coincides with that in random matrix theory. For $\alpha^2/N < N$, the transition shows a marked deviation from random matrix theory. Further, the speed of this transition as a function of the magnetic field is significantly enhanced as $\alpha^2/N$ decreases.