Enhancement in breaking of time-reversal invariance in the quantum kicked rotor

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 noninvariance (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 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.

Automated summary

In this study, the breaking of time-reversal invariance in the quantum kicked rotor by the application of a magnetic field was investigated using a finite-dimensional model. The transition from time-reversal invariance to noninvariance in the spectral and eigenvector fluctuations of the quantum kicked rotor was found to be dependent on the ratio of alpha 2/N, where alpha represents the chaos parameter and N is the dimensionality of the evolution operator matrix. The speed of this transition significantly increases as alpha 2/N decreases, showing deviations from random matrix theory in certain cases.