The non-Markovian stochastic Schrodinger equation for open systems

Abstract

We present the non-Markovian generalization of the widely used stochastic Schrodinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without approximation. Moreover, it unifies two recent independent attempts towards a stochastic description of non-Markovian open systems, based on path integrals on the one hand and coherent states on the other. The latter approach utilizes the analytical properties of coherent states and enables a microscopic interpretation of the stochastic states. The alternative first approach is based on the general description of open systems using path integrals as originated by Feynman and Vernon.

9 pages, RevTeX

References in corpus (1)

• Macroscopic quantum damping in SQUID rings

Cited by in corpus (155)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Dynamical Reduction Models
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Non-Markovian Quantum State Diffusion
• Open system dynamics with non-Markovian quantum trajectories
• Stochastic wave function method for non-Markovian quantum master equations
• Fundamental Aspects of Quantum Brownian Motion
• Exact c-number Representation of Non-Markovian Quantum Dissipation
• Non-Markovian quantum state diffusion: Perturbation approach
• Hierarchy of stochastic pure states for open quantum system dynamics
• Quantum stochastic processes and quantum non-Markovian phenomena
• Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited
• Non-Markovian Quantum Trajectories Versus Master Equations: Finite Temperature Heat Bath
• Time-Dependent Density Matrix Renormalization Group Algorithms for Nearly Exact Absorption and Fluorescence Spectra of Molecular Aggregates at Both Zero and Finite Temperature
• Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach
• Influence of Complex Exciton-Phonon Coupling on Optical Absorption and Energy Transfer of Quantum Aggregates
• Optimized auxiliary oscillators for the simulation of general open quantum systems
• Collapse models with non-white noises
• Suppression of quantum oscillations and the dependence on site energies in electronic excitation transfer in the Fenna-Matthews-Olson trimer
• Quantum trajectories for Brownian motion
• Non-Markovian stochastic Schrödinger equations: Generalization to real-valued noise using quantum measurement theory
• An efficient method to calculate excitation energy transfer in light harvesting systems. Application to the FMO complex
• General Non-Markovian structure of Gaussian Master and Stochastic Schrödinger Equations
• Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)
• Dynamics of quantum dissipation systems interacting with Fermion and Boson grand canonical bath ensembles: Hierarchical equations of motion approach
• Non-Markovian continuous quantum measurement of retarded observables
• The interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory
• Multi-set matrix product state calculations reveal mobile Franck-Condon excitations under strong Holstein-type coupling
• Multiple-time correlation functions for non-Markovian interaction: Beyond the Quantum Regression Theorem
• Non-Markovian quantum state diffusion for absorption spectra of molecular aggregates
• A stochastic approach to open quantum systems
• Internal dissipation and heat leaks in quantum thermodynamic cycles
• Hierarchical equations for open system dynamics in fermionic and bosonic environments
• Nonperturbative Leakage Elimination Operators and Control of a Three-Level System
• Exact non-Markovian master equations for multiple qubit systems: quantum trajectory approach
• Non-Markovian Quantum State Diffusion for Temperature-Dependent Linear Spectra of Light Harvesting Aggregates
• Decoherence and the Nature of System-Environment Correlations
• Dynamical Reduction Models with General Gaussian Noises
• Fast shuttling of a trapped ion in the presence of noise
• Local Temperatures Out of Equilibrium
• Non Markovian Quantum Repeated Interactions and Measurements
• Many-body quantum state diffusion for non-Markovian dynamics in strongly interacting systems
• Time-Local Quantum-State-Diffusion Equation for Multilevel Quantum Dynamics
• Unitary evolution with fluctuations and dissipation
• Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation
• The hierarchical and perturbative forms of stochastic Schrödinger equations and their applications to carrier dynamics in organic materials
• Fundamental Speed Limits to the Generation of Quantumness
• Sublinear scaling in non-Markovian open quantum systems simulations
• Exact propagation of open quantum systems in a system-reservoir context
• Stochastic Schrödinger equations with coloured noise
• Non-Markovian Stochastic Schrödinger Equation: Matrix Product State Approach to the Hierarchy of Pure States
• Quantum parameter estimation in a dissipative environment
• Magnon-mediated quantum battery under systematic errors
• Exact solution for a non-Markovian dissipative quantum dynamics
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
• Dissipative collapse models with non-white noises
• Non-Markovian Quantum Dynamics in Strongly Coupled Multimode Cavities Conditioned on Continuous Measurement
• Non-Markovian quantum trajectories for spectral detection
• Non-Markovian Fermionic Stochastic Schrödinger Equation for Open System Dynamics
• Non-Markovian Open Quantum Systems: Input-Output Fields, Memory, Monitoring
• A perturbative approach to non-Markovian stochastic Schrödinger equations
• Rate operator unravelling for open quantum system dynamics
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model
• Non-Markovian Quantum Trajectories of Many-Body Quantum Open Systems
• Inverse Engineering Control in Open Quantum Systems
• Towards a dynamical approach to the calculation of the figure of merit of thermoelectric nanoscale devices
• Non-Perturbative Quantum Dynamical Decoupling
• Emission spectra of atoms with non-Markovian interaction: Fluorescence in a photonic crystal
• A tomographic approach to non-Markovian master equations
• Fingerprint and universal Markovian closure of structured bosonic environments
• Stochastic Bloch-Redfield theory: quantum jumps in a solid-state environment
• Quantum measurements in continuous time, non Markovian evolutions and feedback
• Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models
• Stochastic Schroedinger Equations with General Complex Gaussian Noises
• Control relaxation via dephasing: an exact quantum state diffusion study
• Optimal control of quantum gates in an exactly solvable non-Markovian open quantum bit system
• Non-adiabatic elimination of auxiliary modes in continuous quantum measurements
• Stochastic unraveling of positive quantum dynamics
• Jump-like unravelings for non-Markovian open quantum systems
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion
• Parametrization and optimization of Gaussian non-Markovian unravelings for open quantum dynamics
• Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems
• Recursive approach for non-Markovian time-convolutionless master equations
• Simulating optical linear absorption for mesoscale molecular aggregates: an adaptive hierarchy of pure states approach
• Functional Lagrange formalism for time-non-local Lagrangians
• Reconstruction of time-dependent coefficients: a check of approximation schemes for non-Markovian convolutionless dissipative generators
• Feshbach Projection Operator Partitioning for Quantum Open Systems: Stochastic Approach
• Quantum trajectories: memory and continuous observation
• Collision model for non-Markovian quantum trajectories
• Nonperturbative stochastic dynamics driven by strongly correlated colored noises
• Does gravity have to be quantized? Lessons from non-relativistic toy models
• Validity of Born-Markov master equations for single and two-qubit systems
• Simulation of absorption spectra of molecular aggregates: a Hierarchy of Stochastic Pure States approach
• Holstein polaron transport from numerically "exact" real-time quantum dynamics simulations
• Stochastic Schrödinger Equations for Markovian and non-Markovian cases
• Solving non-Markovian open quantum systems with multi-channel reservoir coupling
• Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems
• Flexible scheme to truncate the hierarchy of pure states
• Jump-diffusion unravelling of a non Markovian generalized Lindblad master equation
• Realization of hierarchical equations of motion from stochastic perspectives
• Stochastic unravellings of non-Markovian completely positive and trace preserving maps
• General quantum-classical dynamics as measurement based feedback
• System-environment correlations for dephasing two-qubit states coupled to thermal baths
• Spectral properties of molecular oligomers. A non-Markovian quantum state diffusion approach
• Non-Markovian homodyne-mediated feedback on a two-level atom: a quantum trajectory treatment
• Quantum dynamics in a tiered non-Markovian environment
• Non-Markovian quantum trajectories, instruments and time-continuous measurements
• Stable bipolarons in open quantum systems
• Stochastic learning control of adiabatic speedup in a non-Markovian open qutrit system
• Decoherence of Semiclassical Wigner Functions
• General Framework for the Behaviour of Continuously Observed Open Quantum Systems
• Time-Correlated Blip Dynamics of Open Quantum Systems
• Local disclosure of quantum memory in non-Markovian dynamics
• Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise
• Random Control over Quantum Open Systems
• Non-Markovian Quantum State Diffusion for Spin Environments
• Non-Markovian Entanglement Sudden Death and Rebirth of a Two-Qubit System in the Presence of System-Bath Coherence
• On the effectiveness of the collapse in the Diósi-Penrose model
• Effects of non-Markovian squeezed bath on the dynamics of open systems
• Time-local unraveling of non-Markovian stochastic Schrödinger equations
• Non-Markovian environment induced Schrödinger cat state transfer in an optical Newton's cradle
• Probing internal bath dynamics by a Rabi oscillator-based detector
• Symmetries of general non-Markovian Gaussian diffusive unravelings
• Stochastic decoupling approach to the quantum dissipative dynamics: Perturbative and non-perturbative treatments
• Non-stochastic matrix Schrödinger equation for open systems
• Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems
• Excitation Transport in Molecular Aggregates with thermal motion
• Mutual Preservation of Entanglement
• Practical quantum simulation of small-scale non-Hermitian dynamics
• Application of a time-convolutionless stochastic Schrödinger equation to energy transport and thermal relaxation
• Analytical model of non-Markovian decoherence in donor-based charge quantum bits
• Stochastic Schrödinger Equation for a Non-Markovian Dissipative Qubit-Qutrit System
• Connecting two jumplike unravelings for non-Markovian open quantum systems
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Work, heat and entropy production along quantum trajectories
• On the unraveling of open quantum dynamics
• Long-time memory effects in a localizable central spin problem
• Temperature Controlled Open Quantum System Dynamics using Time-dependent Variational Method
• From Stochastic Hamiltonian to Quantum Simulation: Exploring Memory Effects in Exciton Dynamics
• Optimally controlled non-adiabatic quantum state transmission in the presence of quantum noise
• Spectral signatures of the Markovian to Non-Markovian transition in open quantum systems
• Relativistic formulation of quantum state diffusion?
• Input-Output Hierarchical Equations Of Motion
• Reproducing Kernel Hilbert Space Approach to Non-Markovian Quantum Stochastic Models
• Fermionic duality: General symmetry of open systems with strong dissipation and memory
• On the Noisy Road to Open Quantum Dynamics: The Place of Stochastic Hamiltonians
• Stochastic Wave-Function Simulation of Irreversible Emission Processes for Open Quantum Systems in a Non-Markovian Environment
• Quantum correlations between distant qubits conveyed by large-$S$ spin chains
• Perturbation theory under the truncated Wigner approximation reveals how system-environment entanglement formation drives quantum decoherence
• Probabilistic Unitary Formulation of Open Quantum System Dynamics
• Non-Markovian wave-function collapse models are Bohmian-like theories in disguise
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
• Reduced Operator Approximation for Modelling Open Quantum Systems
• Non-Markovian dynamics in nonstationary Gaussian baths: a hierarchy of pure states approach
• Decoherence Effect of Qubits in 1D Transverse Ising Model