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

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 $\to$ 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.

References in corpus (3)

• General phase spaces: from discrete variables to rotor and continuum limits
• Statistical properties of the localization measure in a finite-dimensional model of the quantum kicked rotator
• Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors