Passage times, exit times and Dirichlet problems for open quantum walks

DOI10.1007/s10955-017-1749-3zbMath1376.82085arXiv1610.06772OpenAlexW3103852480MaRDI QIDQ2409994

Denis Bernard, Ivan Bardet, Yan Pautrat

Publication date: 16 October 2017

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.06772

zbMATH Keywords

completely positive mapsopen quantum walksquantum trajectoriesquantum Markov chains

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Open systems, reduced dynamics, master equations, decoherence (81S22)

Related Items (13)

Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions ⋮ On a generalized central limit theorem and large deviations for homogeneous open quantum walks ⋮ Quantum walk and its application domains: a systematic review ⋮ Potential theory for quantum Markov states and other quantum Markov chains ⋮ Open quantum random walks on the half-line: the Karlin-McGregor formula, path counting and Foster's theorem ⋮ Concentration inequalities for output statistics of quantum Markov processes ⋮ Quantum Markov chains on the line: matrix orthogonal polynomials, spectral measures and their statistics ⋮ Recurrence and Transience of Continuous-Time Open Quantum Walks ⋮ Open quantum random walks and quantum Markov chains ⋮ On period, cycles and fixed points of a quantum channel ⋮ Quantum Markov chains: recurrence, Schur functions and splitting rules ⋮ Open quantum random walks, quantum Markov chains and recurrence ⋮ Mean hitting times of quantum Markov chains in terms of generalized inverses

Cites Work

• Open quantum random walks
• Open quantum random walks: ergodicity, hitting times, gambler's ruin and potential theory
• Homogeneous open quantum random walks on a lattice
• Functional analysis, Sobolev spaces and partial differential equations
• The peripheral point spectrum of Schwarz operators on C*-algebras
• Finitely correlated states on quantum spin chains
• Stopping times for quantum Markov chains
• Non-commutative symmetric Markov semigroups
• The noncommutative Markovian property
• Superderivations and symmetric Markov semigroups
• Transience and recurrence of quantum Markov semigroups
• Limit theorems for open quantum random walks
• Open quantum walks on graphs
• Recurrence for discrete time unitary evolutions
• Continuous time open quantum random walks and non-Markovian Lindblad master equations
• On a class of quantum channels, open random walks and recurrence
• Quantum feedback: theory, experiments, and applications
• Site recurrence of open and unitary quantum walks on the line
• Central limit theorems for open quantum random walks and quantum measurement records
• A note on unitary operators in \(C^ *\)-algebras
• Quantum stochastic processes. II
• The open quantum Brownian motions
• Random Walk: A Modern Introduction
• Spectral Properties of Positive Maps on C^* -Algebras
• Markov Chains
• A pathwise ergodic theorem for quantum trajectories
• Open quantum random walks, quantum Markov chains and recurrence
• Dirichlet Forms on Noncommutative Spaces
• Probability
• Open quantum random walks: reducibility, period, ergodic properties
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