Preservation of Positivity by Dynamical Coarse-Graining
arXiv:0804.2374 · doi:10.1103/PhysRevA.78.022106
Abstract
We compare different quantum Master equations for the time evolution of the reduced density matrix. The widely applied secular approximation (rotating wave approximation) applied in combination with the Born-Markov approximation generates a Lindblad type master equation ensuring for completely positive and stable evolution and is typically well applicable for optical baths. For phonon baths however, the secular approximation is expected to be invalid. The usual Markovian master equation does not generally preserve positivity of the density matrix. As a solution we propose a coarse-graining approach with a dynamically adapted coarse graining time scale. For some simple examples we demonstrate that this preserves the accuracy of the integro-differential Born equation. For large times we analytically show that the secular approximation master equation is recovered. The method can in principle be extended to systems with a dynamically changing system Hamiltonian, which is of special interest for adiabatic quantum computation. We give some numerical examples for the spin-boson model of cases where a spin system thermalizes rapidly, and other examples where thermalization is not reached.
18 pages, 7 figures, reviewers suggestions included and tightened presentation; accepted for publication in PRA
References in corpus (22)
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- Quantum Mechanics helps in searching for a needle in a haystack
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
- Maintaining coherence in Quantum Computers
- Robustness of adiabatic quantum computation
- Coherent and Collective Quantum Optical Effects in Mesoscopic Systems
- Bounds for the adiabatic approximation with applications to quantum computation
- Exact time evolution and master equations for the damped harmonic oscillator
- From Completely Positive Maps to the Quantum Markovian Semigroup Master Equation
- Completely Positive Quantum Dissipation
- Thermally assisted adiabatic quantum computation
- Adiabatic Transfer of Electrons in Coupled Quantum Dots
- Staying positive: going beyond Lindblad with perturbative master equations
- Adiabatic quantum algorithms as quantum phase transitions: first versus second order
- General error estimate for adiabatic quantum computing
- Post-Markov master equation for the dynamics of open quantum systems
- Simulation of many-qubit quantum computation with matrix product states
- Spin-boson dynamics beyond conventional perturbation theories
- Positive Quantum Brownian Evolution
- Decoherence versus Dynamical Casimir Effect
- Spin-boson dynamics: A unified approach from weak to strong coupling
- Robust quantum searching with spontaneously decaying qubits
Cited by in corpus (93)
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping
- Quantum thermal absorption machines: refrigerators, engines and clocks
- Accuracy Assessment of Perturbative Master Equations -- Embracing Non-Positivity
- Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
- Entangling two unequal atoms through a common bath
- Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
- Coarse-Graining Can Beat the Rotating Wave Approximation in Quantum Markovian Master Equations
- A thermodynamically consistent Markovian master equation beyond the secular approximation
- Waiting time distributions for the transport through a quantum dot tunnel coupled to one normal and one superconducting lead
- Transport Statistics of Interacting Double Dot Systems: Coherent and Non-Markovian Effects
- Quantum Markovian master equations: resonance theory shows validity for all time scales
- Density-matrix theory of the optical dynamics and transport in quantum cascade structures: The role of coherence
- Fluctuation theorems for capacitively coupled electronic currents
- Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
- Weak coupling approximations in non-Markovian Transport
- Refrigeration beyond weak internal coupling
- Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems
- Lindbladian approximation beyond ultra-weak coupling
- Refined Weak Coupling Limit: Coherence, Entanglement and Non-Markovianity
- An electronic Maxwell demon in the coherent strong-coupling regime
- Harvesting large scale entanglement in de Sitter space with multiple detectors
- Systematic Perturbation Theory for Dynamical Coarse-Graining
- Non-Markovian finite-temperature two-time correlation functions of system operators of a pure-dephasing model
- Symmetry and block structure of the Liouvillian superoperator in partial secular approximation
- Environment induced entanglement in a refined weak-coupling limit
- Master Equations for Electron Transport: The Limits of the Markovian Limit
- Quantum Thermodynamics with Degenerate Eigenstate Coherences
- Local master equations bypass the secular approximation
- Correlation Picture Approach to Open-Quantum-System Dynamics
- Open system dynamics from thermodynamic compatibility
- Interaction effect on adiabatic pump of charge and spin in quantum dot
- Adiabatic preparation without Quantum Phase Transitions
- A low-dimensional detector model for full counting statistics: Trajectories, Back-Action, and Fidelity
- Counting Statistics in Multi-stable Systems
- Entanglement dynamics in de Sitter spacetime
- Double quantum dot coupled to a quantum point contact: A stochastic thermodynamics approach
- Transport with ultracold atoms at constant density
- Full counting statistics and coherences: fluctuation symmetry in heat transport with the Unified quantum master equation
- Going beyond Local and Global approaches for localized thermal dissipation
- Geometric-Arithmetic Master Equation in Large and Fast Open Quantum Systems
- A time-dependent regularization of the Redfield equation
- Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact
- Localized exciton-polariton modes in dye-doped nanospheres: a quantum approach
- Maxwell's demon in the quantum-Zeno regime and beyond
- Reconstruction of Markovian Master Equation parameters through symplectic tomography
- Non-Markovian dynamics under time-translation symmetry
- Quantum Thermodynamics in the Refined Weak Coupling Limit
- Quantum Equilibration under Constraints and Transport Balance
- Single Spin Transport Spectroscopy - Current Blockade and Spin Decay
- Error Suppression for Hamiltonian Quantum Computing in Markovian Environments
- Invalidation of the Bloch-Redfield Equation in Sub-Ohmic Regime via a Practical Time-Convolutionless Fourth-Order Master Equation
- Excess entropy production in quantum system: Quantum master equation approach
- Fighting Decoherence by Feedback-controlled Dissipation
- Nonclassical light from few emitters in a cavity
- Ergodic-localized junctions in periodically-driven systems
- Master equation for high-precision spectroscopy
- Quantum master equation for many-body systems: Derivation based on the Lieb-Robinson bound
- Coarse-graining master equation for periodically driven systems
- Decoherence in a dynamical quantum phase transition
- Recovering complete positivity of non-Markovian quantum dynamics with Choi-proximity regularization
- Construction of propagators for divisible dynamical maps
- Environmentally Induced Entanglement -- Anomalous Behavior in the Adiabatic Regime
- Dynamics of the Non-equilibrium spin Boson Model: A Benchmark of master equations and their validity
- Dynamics of Micro and Nanoscale Systems in the Weak-Memory Regime
- Thermodynamics of the Coarse-Graining Master Equation
- Dynamic Stark effect, light emission, and entanglement generation in a laser-driven quantum optical system
- Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
- Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
- Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks
- Transport as a sensitive indicator of quantum criticality
- Semiclassical spin-spin dynamics and feedback control in transport through a quantum dot
- On the standard quantum Brownian equation and an associated class of non-autonomous master equations
- The speed of Markovian relaxation towards the ground state
- Completely Positive Map for Noisy Driven Quantum Systems Derived by Keldysh Expansion
- Stochastically bundled dissipators for the quantum master equation
- Open system dynamics in interacting quantum field theories
- Derivation of Markovian master equation by renormalization group method
- Decoherence Strength of Multiple Non-Markovian Environments
- Dynamics of micro and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation
- Open quantum systems and the grand canonical ensemble
- Non-Markovian dynamics of few emitters in a laser-driven cavity
- Strong Markov dissipation in driven-dissipative quantum systems
- Generation, dynamical buildup and detection of bi- and mulipartite entangled states in cavity systems
- Finite-time performance of a cyclic 2d quantum Ising heat engine
- Permutationally invariant processes in open multiqudit systems
- Open harmonic chain without secular approximation
- Davies equation without the secular approximation: Reconciling locality with quantum thermodynamics for open quadratic systems
- Error bounds on the universal Lindblad equation in the thermodynamic limit
- Preprocessing operations and the reverse compression
- Finite speed heat transport in a quantum spin chain after quenched local cooling
- Preserving fermionic statistics for single-particle approximations in microscopic quantum master equations
- Open quantum systems beyond equilibrium: Lindblad equation and path integral molecular dynamics