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arXiv · 2111.05706

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

Ramgopal Agrawal·Akhilesh Pandey·Sanjay Puri
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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.

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Ramgopal Agrawal, Akhilesh Pandey, Sanjay Puri. 2021-11-10. Enhancement in Breaking of Time-reversal Invariance in the Quantum Kicked Rotor. https://doi.org/10.1103/physreve.104.064202

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