Exponentially decaying velocity bounds of quantum walks in periodic fields

DOI10.1007/s00220-023-04840-4arXiv2302.01869MaRDI QIDQ6076987

Houssam M. Abdul-Rahman, Günter Stolz

Publication date: 17 October 2023

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.01869

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Discrete-time Markov processes on general state spaces (60J05) Periodic solutions to ordinary differential equations (34C25) General and philosophical questions in quantum theory (81P05) Unitary representations of locally compact groups (22D10) Local ground fields in algebraic geometry (14G20) Associative rings of fractions and localizations (16S85)

Cites Work

• Unnamed Item
• Unnamed Item
• Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line
• Dynamical localization of quantum walks in random environments
• Dynamical localization for unitary Anderson models
• One-dimensional discrete-time quantum walks on random environments
• Spectral analysis of unitary band matrices
• Correlated Markov quantum walks
• Stability of driven systems with growing gaps, quantum rings, and Wannier ladders.
• Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
• Density of states and Thouless formula for random unitary band matrices
• Cantor spectrum for CMV matrices with almost periodic Verblunsky coefficients
• Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients
• Anderson localization for electric quantum walks and skew-shift CMV matrices
• Quantum dynamics of periodic and limit-periodic Jacobi and block Jacobi matrices with applications to some quantum many body problems
• CMV matrices: Five years after
• Localization for random unitary operators
• Spectral transition for random quantum walks on trees
• A Floquet operator with purely point spectrum and energy instability
• Fractional moment estimates for random unitary operators
• Disordered quantum walks in one lattice dimension
• Random Unitary Models and their Localization Properties
• Universal Computation by Multiparticle Quantum Walk
• Lyapunov exponents for unitary Anderson models
• Motion in periodic potentials
• Quantum walks in external gauge fields
• Asymptotic evolution of quantum walks with random coin
• Quantum Walks
• Quantum walks and search algorithms
• Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices

This page was built for publication: Exponentially decaying velocity bounds of quantum walks in periodic fields