Expansion of time-convolutionless non-Markovian quantum master equations: A case study using the Fano-Anderson model
arXiv:2604.22010 · doi:10.1063/5.0323348
Abstract
We explore the performance of the time-convolutionless (TCL) projection operator technique using the Fano-Anderson model as a test case. Comparing the exact TCL master equation with an expansion in powers of the strength of the system-environment coupling, we analyze the transient dynamics as well as the steady-state behavior. For a Lorentzian spectral density we demonstrate that the dimensionless expansion parameter corresponds to the ratio of the environmental correlation time to the relaxation time of the system, and we derive the convergence radius for the TCL expansion, which is seen to depend on the ratio of detuning and width of the spectral density. We further study the quantum non-Markovianity of the model based on the evolution of the Bures distance between quantum states and how it is represented by the second and fourth order of the expansion. Our results highlight both the strengths and the limitations of the TCL formalism in capturing key features of open quantum systems and, in particular, the challenges of accurately describing strongly coupled systems and non-Markovian dynamics.
13 pages, 13 figures
References in corpus (24)
- Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
- Non-Markovian dynamics in open quantum systems
- Entanglement and non-Markovianity of quantum evolutions
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Quantum Thermodynamics
- Measure for the Non-Markovianity of Quantum Processes
- Canonical form of master equations and characterization of non-Markovianity
- General non-Markovian dynamics of open quantum systems
- Stochastic wave function method for non-Markovian quantum master equations
- Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
- Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
- A non-Markovian decoherence theory for double dot charge qubit
- Foundations and Measures of Quantum Non-Markovianity
- Quantifying non-Markovianity of continuous variable Gaussian dynamical maps
- A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach
- Open-system approach to nonequilibrium quantum thermodynamics at arbitrary coupling
- Precursors of non-Markovianity
- Entropic bounds on information backflow
- Non-Markovianity of Quantum Brownian Motion
- Dynamically Emergent Quantum Thermodynamics: Non-Markovian Otto Cycle
- Thermodynamic Roles of Quantum Environments: From Heat Baths to Work Reservoirs
- Markovian and non-Markovian master equations versus an exactly solvable model of a qubit in a cavity
- Unveiling coherent dynamics in non-Markovian open quantum systems: exact expression and recursive perturbation expansion
- Recursive perturbation approach to time-convolutionless master equations: Explicit construction of generalized Lindblad generators for arbitrary open systems