The Accuracy of Perturbative Master Equations

Abstract

We consider open quantum systems with dynamics described by master equations that have perturbative expansions in the system-environment interaction. We show that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation. We give two examples of such inaccuracies in the solutions to an order-2n master equation: order-2n inaccuracies in the steady state of the system and order-2n positivity violations, and we show how these arise in a specific example for which exact solutions are available. This result has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.

6 pages, 0 figures; v2 updated references; v3 updated references, extension to full-time and nonlocal regimes

References in corpus (5)

• Non-Markovian quantum dynamics: local versus non-local
• Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited
• Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
• The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis
• Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation

Cited by in corpus (51)

• Delocalized excitons in natural light harvesting complexes
• Nonequilibrium Green's function method for quantum thermal transport
• Accuracy Assessment of Perturbative Master Equations -- Embracing Non-Positivity
• Open quantum system dynamics and the mean force Gibbs state
• Perturbative approach to Markovian open quantum systems
• The equilibrium states of open quantum systems in the strong coupling regime
• Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths
• Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
• Tunable phonon induced steady state coherence in a double quantum dot
• Weak and ultrastrong coupling limits of the quantum mean force Gibbs state
• A multi-site variational master equation approach to dissipative energy transfer
• Tensor-network method to simulate strongly interacting quantum thermal machines
• Reduced density matrix for nonequilibrium steady states: A modified Redfield solution approach
• Non-Markovian Dynamics of Open Quantum Systems: Stochastic Equations and their Perturbative Solutions
• Coarse Grained Quantum Dynamics
• Steady state thermal transport in anharmonic systems: Application to molecular junctions
• Open Quantum System Dynamics from Infinite Tensor Network Contraction
• Canonically consistent quantum master equation
• Improved Dyson series expansion for steady-state quantum transport beyond the weak coupling limit - divergences and resolution
• Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
• Effects of electron-phonon interaction on thermal and electrical transport through molecular nano-conductors
• Hamiltonian of mean force in the weak-coupling and high-temperature approximations and refined quantum master equations
• Non-Markovian Dynamics and Entanglement of Two-level Atoms in a Common Field
• Numerical evaluation and robustness of the quantum mean force Gibbs state
• A Lindblad Model of Quantum Brownian Motion
• Lyapunov equation in open quantum systems and non-Hermitian physics
• Exactness of the mean-field dynamics in optical cavity systems
• Finite coupling effects in double quantum dots near equilibrium
• Dissipative time crystals originating from parity-time symmetry
• Perturbative Steady States of Completely Positive Quantum Master Equations
• Initial state preparation with dynamically generated system-environment correlations
• Invalidation of the Bloch-Redfield Equation in Sub-Ohmic Regime via a Practical Time-Convolutionless Fourth-Order Master Equation
• Multiple-scale analysis of open quantum systems
• Transport and energetic properties of a ring of interacting spins coupled to heat baths
• Spin rectification in thermally driven XXZ spin chain via the spin-Seebeck effect
• Corrections to the Hamiltonian induced by finite-strength coupling to the environment
• Typical, finite baths as a means of exact simulation of open quantum systems
• Dynamics of the Non-equilibrium spin Boson Model: A Benchmark of master equations and their validity
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Master equation based steady-state cluster perturbation theory
• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Decoherence Strength of Multiple Non-Markovian Environments
• Transport in Conductors and Rectifiers: Mean-Field Redfield Equations and Non-Equilibrium Green's Functions
• Natural correlation between a system and a thermal reservoir
• Global becomes local: Efficient many-body dynamics for global master equations
• Full-polaron master equation approach to dynamical steady states of a driven two-level system beyond the weak system-environment coupling
• Gate-Based Initialization and Fidelity in Correlated Open Quantum Systems
• Nonclassical radiation from a nonlinear oscillator driven solely by classical $1/f$ noise
• Weak-Memory Dynamics in Discrete Time
• Semidefinite programming for understanding the limitations of Lindblad equations