Quantum Semi-Markov Processes

Abstract

We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow the treatment of a variety of physical systems, as is illustrated by means of various examples and applications, including quantum optical systems and models of quantum transport.

4 pages, revtex, no figures, to appear in Phys. Rev. Lett

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Cited by in corpus (82)

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• Measure for the Non-Markovianity of Quantum Processes
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• On measures of non-Markovianity: divisibility vs. backflow of information
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• Markovian and non-Markovian dynamics in quantum and classical systems
• Optimal state pairs for non-Markovian quantum dynamics
• Exact master equations for the non-Markovian decay of a qubit
• Witness for initial system-environment correlations in open system dynamics
• Master equations for correlated quantum channels
• Initial correlations in open system's dynamics: The Jaynes-Cummings model
• Measuring non-Markovianity of processes with controllable system-environment interaction
• Non-Markovian random unitary qubit dynamics
• Completely positive master equation for arbitrary driving and small level spacing
• Non-Markovianity degree for random unitary evolution
• Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system
• Structure of completely positive quantum master equations with memory kernel
• Equivalence of the measures of non-Markovianty for open two-level systems
• Phenomenological memory-kernel master equations and time-dependent Markovian processes
• Generalized master equations leading to completely positive dynamics
• Proposed method for direct measurement of non-Markovian character of the qubits coupled to bosonic reservoirs
• All-optical non-Markovian stroboscopic quantum simulator
• Long-time memory in non-Markovian evolutions
• Non-Markovian master equations from piecewise dynamics
• Dissipative dynamics of a solid-state qubit coupled to surface plasmons: from non-Markov to Markov regimes
• Sufficient conditions for memory kernel master equation
• Tomographically reconstructed master equations for any open quantum dynamics
• Stochastic jump processes for non-Markovian quantum dynamics
• Markovianity criteria for quantum evolution
• A classical appraisal of quantum definitions of non-Markovian dynamics
• Interaction-induced correlations and non-Markovianity of quantum dynamics
• Non Markovian Quantum Repeated Interactions and Measurements
• Quantum discord and non-Markovianity of quantum dynamics
• Markovian embedding of non-Markovian quantum collisional models
• Exact solution for a non-Markovian dissipative quantum dynamics
• On generalized semi-Markov quantum evolution
• On admissible memory kernels for random unitary qubit evolution
• Quantum non-Markovian piecewise dynamics from collision models
• Non-Markovian non-stationary completely positive open quantum system dynamics
• Open system dynamics from thermodynamic compatibility
• Rate operator unravelling for open quantum system dynamics
• The interplay between local and non-local master equations: exact and approximated dynamics
• Singularity of dynamical maps
• Decoherence suppression of a dissipative qubit by the non-Markovian effect
• Quantum thermo-dynamical construction for driven open quantum systems
• Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond
• Convex combinations of CP-divisible Pauli channels that are not semigroups
• Non-Markovian dynamics for an open two-level system without rotating wave approximation: Indivisibility versus backflow of information
• Witnessing non-Markovianity of quantum evolution
• Recursive approach for non-Markovian time-convolutionless master equations
• Post-Markovian quantum master equations from classical environment fluctuations
• Exploring initial correlations in a Gibbs state by local application of external field
• Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
• Time deformations of master equations
• Multi-mode entanglement of N harmonic oscillators coupled to a non-Markovian reservoir
• Approximating open quantum system dynamics in a controlled and efficient way: A microscopic approach to decoherence
• Non-divisiblity and non-Markovianity in a Gaussian dissipative dynamics
• Quantum renewal processes
• Reduced Dynamics of Full Counting Statistics
• Local disclosure of quantum memory in non-Markovian dynamics
• Evolution equations for quantum semi-Markov dynamics
• Asymptotic Floquet states of non-Markovian systems
• Non-Markovian entanglement dynamics in coupled superconducting qubit systems
• Microscopic modelling of general time-dependent quantum Markov processes
• Algorithmic quantum simulation of memory effects
• A solvable class of non-Markovian quantum multipartite dynamics
• Born-Oppenheimer approximation in open systems
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Memory effects in quantum dynamics modelled by quantum renewal processes
• Signatures of non-Markovianity in classical single-time probability distributions
• On the hybrid Davies like generator for quantum dissipation
• Continuous stochastic processes with non-local memory
• Non-Markovian Equilibration Controlled by Symmetry Breaking
• Complete positivity, positivity and long-time asymptotic behavior in a two-level open quantum system
• Memory-dependent noise-induced resonance and diffusion in non-markovian systems
• Correlation effects in a discrete quantum random walk
• Non-Markovian open dynamics from collision models
• Frontiers of open quantum system dynamics
• A non-Markovian Dissipative Maryland Model
• Memory effects displayed in the evolution of continuous variable system
• Decoherence dynamics of open qubit systems