Spectral stability of unitary network models
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Publication:3449169
DOI10.1142/S0129055X15300046zbMath1326.81035arXiv1502.02301MaRDI QIDQ3449169
Joachim Asch, Olivier Bourget, Alain Joye
Publication date: 3 November 2015
Published in: Reviews in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1502.02301
Sums of independent random variables; random walks (60G50) Quantum computation (81P68) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Quantum stochastic calculus (81S25) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)
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Cites Work
- Unnamed Item
- Localization of the Grover walks on spidernets and free Meixner laws
- Commutator methods for unitary operators
- Dynamical localization of the Chalker-Coddington model far from transition
- Open quantum random walks
- Spectral and asymptotic properties of Grover walks on crystal lattices
- Commutation relations for unitary operators. I
- Localization properties of the Chalker-Coddington model
- Dynamical localization of quantum walks in random environments
- Random time-dependent quantum walks
- Index theory of one dimensional quantum walks and cellular automata
- Dynamical localization for unitary Anderson models
- Floquet operators without singular continuous spectrum
- One-dimensional discrete-time quantum walks on random environments
- Absence of singular continuous spectrum for certain self-adjoint operators
- The Mourre theory for analytically fibered operators
- Spectral analysis of unitary band matrices
- Quantum walks: a comprehensive review
- Dynamical localization for \(d\)-dimensional random quantum walks
- Correlated Markov quantum walks
- Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
- Density of states and Thouless formula for random unitary band matrices
- Scattering zippers and their spectral theory
- Recurrence for discrete time unitary evolutions
- Dynamics of unitary operators
- Localization for random unitary operators
- Spectral transition for random quantum walks on trees
- A Floquet operator with purely point spectrum and energy instability
- Spectral properties of quantum walks on rooted binary trees
- Disordered quantum walks in one lattice dimension
- Motion in periodic potentials
- ON THE SPECTRAL PROPERTIES OF DISCRETE SCHRÖDINGER OPERATORS
- Asymptotic evolution of quantum walks with random coin
- Quantum Markov chains