Quantifying the influence of the initial state on the dynamics of an open quantum system
arXiv:2211.17149 · doi:10.1103/PhysRevA.107.022211
Abstract
A small system in contact with a macroscopic environment usually approaches an asymptotic state, determined only by some macroscopic properties of the environment such as the temperature or the chemical potential. In the long-time limit, the state of the small system is thus expected to be independent of its initial state. In some situations, however, the asymptotic state of the system is influenced by its initial state and some information about the initial state is kept for all times. Motivated by this finding, we propose a measure to quantify the influence of the initial state of an open system on its dynamics. Using this measure we derive conditions under which the asymptotic state exists and is unique. We demonstrate our concepts for the dynamics of the spin-boson model, identify three qualitatively different long-time behaviors, and discuss how they can be distinguished based on the proposed measure.
arXiv comment12 pages, 6 figures
References in corpus (27)
- Many body localization and thermalization in quantum statistical mechanics
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Decoherence Free Subspaces for Quantum Computation
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Effective quantum spin systems with ion traps
- Prescription for experimental determination of the dynamics of a quantum black box
- Quantum mechanical evolution towards thermal equilibrium
- Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
- The Bloch Vector for N-Level Systems
- Symmetries and conserved quantities in Lindblad master equations
- Quantum Process Tomography: Resource Analysis of Different Strategies
- Multilayer multi-configuration time-dependent Hartree method: implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
- Taming the dynamical sign problem in real-time evolution of quantum many-body problems
- Numerically Exact Long Time Magnetization Dynamics at the Nonequilibrium Kondo Crossover of the Anderson Impurity Model
- Analysis of quantum semigroups with GKS--Lindblad generators II. General
- Mesoscopic Spin-Boson Models of Trapped Ions
- Quantum process tomography and Linblad estimation of a solid state qubit
- Time-resolved observation of thermalization in an isolated quantum system
- Multiple steady-states in nonequilibrium quantum systems with electron-phonon interactions
- Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain
- How to discretize a quantum bath for real-time evolution
- Analysis of quantum semigroups with GKS-Lindblad generators I. Simple generators
- Exact Calculation of the Time Convolutionless Master Equation Generator: Application to the Nonequilibrium Resonant Level Model
- Note: On the memory kernel and the reduced system propagator
- Role of correlations in the thermalization of quantum systems