Density of States and Thouless Formula for Random Unitary Band Matrices

Abstract

We study the density of states measure for some class of random unitary band matrices and prove a Thouless formula relating it to the associated Lyapunov exponent. This class of random matrices appears in the study of the dynamical stability of certain quantum systems and can also be considered as a unitary version of the Anderson model. We further determine the support of the density of states measure and provide a condition ensuring it possesses an analytic density.

References in corpus (4)

• Stability of driven systems with growing gaps, Quantum rings and Wannier ladders
• Absolute Continuity of the Floquet Spectrum for a Nonlinearly Forced Harmonic Oscillator
• Weakly regular Floquet Hamiltonians with pure point spectrum
• Transport properties of kicked and quasi-periodic Hamiltonians

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• Lyapunov Exponents for Unitary Anderson Models
• Quantum Localization in Open Chaotic Systems
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• Thermalization of Fermionic Quantum Walkers
• Spectral Properties of Non-Unitary Band Matrices
• Absence of Bound States for Quantum Walks and CMV Matrices via Reflections
• Lower Bounds on the Localisation Length of Balanced Random Quantum Walks
• Anderson localization for electric quantum walks and skew-shift CMV matrices
• The Statistical Distribution of the Zeros of Random Paraorthogonal Polynomials on the Unit Circle
• A Floquet Operator with Pure Point Spectrum and Energy Instability