Non-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging

Abstract

The time-convolutionless (TCL) projection operator technique allows a systematic analysis of the non-Markovian quantum dynamics of open systems. We introduce a class of projection superoperators which project the states of the total system onto certain correlated system-environment states. It is shown that the application of the TCL technique to this class of correlated superoperators enables the non-perturbative treatment of the dynamics of system-environment models for which the standard approach fails in any finite order of the coupling strength. We demonstrate further that the correlated superoperators correspond to the idea of a best guess of conditional quantum expectations which is determined by a suitable Hilbert space average. The general approach is illustrated by means of the model of a spin which interacts through randomly distributed couplings with a finite reservoir consisting of two energy bands. Extensive numerical simulations of the full Schroedinger equation of the model reveal the power and efficiency of the method.

14 pages, 5 figures

References in corpus (9)

• Stochastic wave function method for non-Markovian quantum master equations
• 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
• Quantum Approach to a Derivation of the Second Law of Thermodynamics
• Distribution of local entropy in the Hilbert space of bi-partite quantum systems: Origin of Jaynes' principle
• Quantum master equation for a system influencing its environment
• Thermalization of quantum systems by finite baths
• From Pure Schroedingerian to Statistical Dynamics

Cited by in corpus (78)

• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Foundations and Measures of Quantum Non-Markovianity
• Non-Markovian generalization of the Lindblad theory of open quantum systems
• Dynamical typicality of quantum expectation values
• Exact master equations for the non-Markovian decay of a qubit
• Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects
• Quantum linear Boltzmann equation
• Quantum Semi-Markov Processes
• Low-temperature thermometry can be enhanced by strong coupling
• 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
• Lindblad rate equations
• Correlated projection operator approach to non-Markovian dynamics in spin baths
• Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
• Internal dissipation and heat leaks in quantum thermodynamic cycles
• Quantum systems correlated with a finite bath: nonequilibrium dynamics and thermodynamics
• Quantum dephasing induced by non-Markovian random telegraph noise
• Non-Markovian dynamics for bipartite systems
• Quantum discord and non-Markovianity of quantum dynamics
• Occurrence of exponential relaxation in closed quantum systems
• Non-Markovian non-stationary completely positive open quantum system dynamics
• Classicality, Markovianity and local detailed balance from pure state dynamics
• Correlation Picture Approach to Open-Quantum-System Dynamics
• Stochastic Wave-Function Unravelling of the Generalized Lindblad Master Equation
• Transition from diffusive to ballistic dynamics for a class of finite quantum models
• Open quantum system approach to single-molecule spectroscopy
• Finite quantum environments as thermostats: an analysis based on the Hilbert space average method
• Quantum master equation for the microcanonical ensemble
• Quantum Thermalization With Couplings
• Reduced dynamical maps in the presence of initial correlations
• Relaxation, thermalization and Markovian dynamics of two spins coupled to a spin bath
• Quantum regression theorem for non-Markovian Lindblad equations
• Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir
• Recursive approach for non-Markovian time-convolutionless master equations
• Quantum trajectories: memory and continuous observation
• Non-Markovian Quantum Jump with Generalized Lindblad Master Equation
• Open quantum systems coupled to finite baths: A hierarchy of master equations
• Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
• Noise gates for decoherent quantum circuits
• Effective Hamiltonian Approach to Open Systems and Its Applications
• Non-Markovian Effects on the Geometric Phase
• Dynamics of open quantum spin systems: An assessment of the quantum master equation approach
• Jump-diffusion unravelling of a non Markovian generalized Lindblad master equation
• Quantifying non-Markovianity due to driving and a finite-size environment in an open quantum system
• Arbitrary spin in a spin bath: Exact dynamics and approximation techniques
• Initial correlation in a system of a spin coupled to a spin bath through an intermediate spin
• A weak-coupling master equation for arbitrary initial conditions
• Quantum Foundations of Classical Reversible Computing
• Probing internal bath dynamics by a Rabi oscillator-based detector
• Fermi's golden rule, the origin and breakdown of Markovian master equations, and the relationship between oscillator baths and the random matrix model
• Quantum master equation from the eigenstate thermalization hypothesis
• Microscopic modelling of general time-dependent quantum Markov processes
• Information of a qubit interacting with a multilevel environment
• Boltzmann equation approach to transport in finite modular quantum systems
• Typical, finite baths as a means of exact simulation of open quantum systems
• Born-Oppenheimer approximation in open systems
• Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization
• Projection operator approach to transport in complex single-particle quantum systems
• Thermal drag in spin ladders coupled to phonons
• Connecting two jumplike unravelings for non-Markovian open quantum systems
• Transport in anisotropic model systems analyzed by a correlated projection superoperator technique
• Parametric approximation as open quantum systems problem
• On the structure of the exact master equation
• Stochastic wave-function unravelling of the generalized Lindblad equation
• Effective environments: Preparation of stationary states with inverse temperature ranging from positive to negative values
• Unfolding system-environment correlation in open quantum systems: Revisiting master equations and the Born approximation
• Hilbert Space Average Method and adiabatic quantum search
• Projection operator approach to master equations for coarse grained occupation numbers in non-ideal quantum gases
• Role of correlations in the thermalization of quantum systems
• Quantum-classical hybrid dynamics: coupling mechanisms and diffusive approximation
• Non-Markovian quantum dynamics: Extended correlated projection superoperators
• On time-dependent projectors and on generalization of thermodynamical approach to open quantum systems
• Effective Hamiltonian approach to the quantum phase transitions in the extended Jaynes-Cummings model
• Correlation effects in a discrete quantum random walk
• A general and solvable random matrix model for spin decoherence
• Harnessing spin-qubit decoherence to probe strongly-interacting quantum systems
• Perturbation theory under the truncated Wigner approximation reveals how system-environment entanglement formation drives quantum decoherence
• Adapted projection operator technique for the treatment of initial correlations