Spectral transition for random quantum walks on trees

DOI10.1007/s00220-014-1882-7zbMath1285.82045arXiv1212.6078OpenAlexW1964949130MaRDI QIDQ2439706

Eman Hamza, Alain Joye

Publication date: 17 March 2014

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

Full work available at URL: https://arxiv.org/abs/1212.6078

zbMATH Keywords

static disorderrandom quantum walkstrong disorder localizationweak disorder delocalization

Mathematics Subject Classification ID

Trees (05C05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)

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Cites Work

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• Dynamical localization of the Chalker-Coddington model far from transition
• Open quantum random walks
• Dynamical localization of quantum walks in random environments
• Random time-dependent quantum walks
• Dynamical localization for unitary Anderson models
• Localization at large disorder and at extreme energies: an elementary derivation
• Extended states in the Anderson model on the Bethe lattice
• Spectral analysis of unitary band matrices
• Quantum walks: a comprehensive review
• Dynamical localization for \(d\)-dimensional random quantum walks
• Correlated Markov quantum walks
• Resonant delocalization for random Schrödinger operators on tree graphs
• Localization for random unitary operators
• Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs
• Fractional moment estimates for random unitary operators
• Disordered quantum walks in one lattice dimension
• Search via Quantum Walk
• Quantum Walk Based Search Algorithms
• LOCALIZATION AT WEAK DISORDER: SOME ELEMENTARY BOUNDS
• Quantum walks on graphs
• Asymptotic evolution of quantum walks with random coin
• Quantum Walks
• Quantum Markov chains
• Limit Theorems for Discrete-Time Quantum Walks on Trees