Non-Markovian generalization of the Lindblad theory of open quantum systems

Abstract

A systematic approach to the non-Markovian quantum dynamics of open systems is given by the projection operator techniques of nonequilibrium statistical mechanics. Combining these methods with concepts from quantum information theory and from the theory of positive maps, we derive a class of correlated projection superoperators that take into account in an efficient way statistical correlations between the open system and its environment. The result is used to develop a generalization of the Lindblad theory to the regime of highly non-Markovian quantum processes in structured environments.

10 pages, 1 figure, replaced by published version

References in corpus (5)

• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Genuine quantum trajectories for non-Markovian processes
• Stochastic Representation of a Class of Non-Markovian Completely Positive Evolutions
• Lindblad rate equations

Cited by in corpus (67)

• Quantum trajectories and open many-body quantum systems
• Foundations and Measures of Quantum Non-Markovianity
• Quantum critical behavior in strongly interacting Rydberg gases
• Exact master equations for the non-Markovian decay of a qubit
• Witness for initial system-environment correlations in open system dynamics
• Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects
• Quantum Semi-Markov Processes
• 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
• Optimal Decoherence Control in non-Markovian Open, Dissipative Quantum Systems
• Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
• Generalized master equations leading to completely positive dynamics
• Non-Markovian dynamics of a qubit coupled to an Ising spin bath
• Optoelectronic device simulations based on macroscopic Maxwell-Bloch equations
• How state preparation can affect a quantum experiment: Quantum process tomography for open systems
• An Efficient Quantum Jump Method for Coherent Energy Transfer Dynamics in Photosynthetic Systems under the Influence of Laser Fields
• Non-Markovian dynamics for bipartite systems
• Quantum discord and non-Markovianity of quantum dynamics
• Non-Markovian non-stationary completely positive open quantum system dynamics
• Stochastic Wave-Function Unravelling of the Generalized Lindblad Master Equation
• Open quantum system approach to single-molecule spectroscopy
• Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• Quantum trajectories: memory and continuous observation
• Quantum master equation for collisional dynamics of massive particles with internal degrees of freedom
• Quantum-jumps and photon-statistic in fluorescent systems coupled to classically fluctuating reservoirs
• Nonperturbative stochastic dynamics driven by strongly correlated colored noises
• Open quantum systems coupled to finite baths: A hierarchy of master equations
• Non-Markovian Quantum Jump with Generalized Lindblad Master Equation
• Noise gates for decoherent quantum circuits
• Effective Hamiltonian Approach to Open Systems and Its Applications
• Non-Markovian Effects on the Geometric Phase
• Quantifying non-Markovianity due to driving and a finite-size environment in an open quantum system
• Riccati equation and the problem of decoherence
• Structured quantum collision models: generating coherence with thermal resources
• Emergence of Opposing Arrows of Time in Open Quantum Systems
• Probing internal bath dynamics by a Rabi oscillator-based detector
• Effective Heisenberg equations for quadratic Hamiltonians
• Noise, delocalization, and quantum diffusion in one-dimensional tight-binding models
• Microscopic modelling of general time-dependent quantum Markov processes
• Detection of Bidirectional System-Environment Information Exchanges
• Lattice mapping for many-body open quantum systems and its application to atoms in photonic cystals
• Projection operator approach to transport in complex single-particle quantum systems
• Kraus decomposition for chaotic environments
• Qubit fidelity under stochastic Schrödinger equations driven by colored noise
• Memory effects in quantum dynamics modelled by quantum renewal processes
• Transport in anisotropic model systems analyzed by a correlated projection superoperator technique
• Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System
• Quantum Dissipative Search via Lindbladians
• Minimalistic analytical approach to non-Markovian open quantum systems
• Gravitationally induced decoherence of a scalar field: investigating the one-particle sector and its interplay with renormalisation
• Effective Hamiltonian approach to the quantum phase transitions in the extended Jaynes-Cummings model
• On time-dependent projectors and on generalization of thermodynamical approach to open quantum systems
• Non-Markovian quantum dynamics: Extended correlated projection superoperators
• Quantum-classical hybrid dynamics: coupling mechanisms and diffusive approximation
• Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schrödinger Equation Approach
• An open scattering model in polymerized quantum mechanics
• Non-Markovian quantum Brownian motion: a non-Hamiltonian approach
• On the use of total state decompositions for the study of reduced dynamics
• A Fractional Calculus Framework for Open Quantum Dynamics: From Liouville to Lindblad to Memory Kernels
• Universal dissipators for driven open quantum systems and the correction to linear response
• Probabilistic Unitary Formulation of Open Quantum System Dynamics
• Weak-Coupling Limit. II On the Quantum Fokker-Planck Equation
• Perturbation theory under the truncated Wigner approximation reveals how system-environment entanglement formation drives quantum decoherence
• Non-equilibrium Dynamics of Three-Level Absorption Refrigerator at Third-Order Liouvillian Exceptional Points
• Quasi non-Markovian approach to the study of decoherence of a controlled-not quantum gate in a chain of few nuclear spins quantum computer
• Adapted projection operator technique for the treatment of initial correlations