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 (15)

• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Statistics of energy levels and eigenfunctions in disordered systems
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron Transport in Chaotic Microstructures
• Dynamical localization in chaotic systems: spectral statistics and localization measure in the kicked rotator as a paradigm for time-dependent and time-independent systems
• General phase spaces: from discrete variables to rotor and continuum limits
• Superintegrability of Geodesic Motion on the Sausage Model
• Measurement of Wave Chaotic Eigenfunctions in the Time-Reversal Symmetry-Breaking Crossover Regime
• Encoding many qubits in a rotor
• 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
• Finite-Range Coulomb Gas Models II: Applications to Quantum Kicked Rotors and Banded Random Matrices
• Finite-Range Coulomb Gas Models I: Some Analytical Results
• Scattering and transport statistics at criticality