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.
12 pages, 6 figures
References in corpus (10)
- Many body localization and thermalization in quantum statistical mechanics
- Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
- 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
- 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
- Analysis of quantum semigroups with GKS-Lindblad generators I. Simple generators
- Role of correlations in the thermalization of quantum systems