Analysis of quantum semigroups with GKS–Lindblad generators: II. General

2008/06/19 by Bernhard Baumgartner, Heide Narnhofer · 7 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1088/1751-8113/41/39/395303

32 pages, 2 figures, ESI Report

arxiv created 2008/06/19 · openalex publication_date 2008/09/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Semigroups describing the time evolution of open quantum systems in finite-dimensional spaces have generators of a special form, known as Lindblad generators. These generators and the corresponding processes of time evolution are analyzed and characterized as decay, dissipation and dephasing. In relation to these processes the Hilbert space of the system is equipped with a special structure, a decomposition into a sum of mutually orthogonal subspaces. The complete set of all the stationary states and the asymptotic behavior of the evolutions are presented in detail. Some unusual special facts about invariant operators and symmetries are studied and examples are demonstrated. Perturbation theory for the structure and for the stationary states is discussed and performed in case studies.

Citations

• Analysis of quantum semigroups with GKS–Lindblad generators: I. Simple generators
• Completely positive dynamical semigroups of N-level systems
• Decoherence, einselection, and the quantum origins of the classical

Cited by

• Symmetry-protected coherent relaxation of open quantum systems
• Time-averaged quantum dynamics and the validity of the effective Hamiltonian model
• Three qubits in a symmetric environment: Dissipatively generated asymptotic entanglement
• Unitary–scaling decomposition and dissipative behaviour in finite-dimensional unital Lindblad dynamics
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
• Dynamical signatures of molecular symmetries in nonequilibrium quantum transport

Related

• The Gorini-Kossakowski-Sudarshan-Lindblad generation theorem,and a generalization to non-stationary evolutions
• State Space Decomposition of Quantum Dynamical Semigroups
• Nonstandard derivation of the Gorini-Kossakowski-Sudarshan-Lindblad master equation of a quantum dynamical semigroup from the Kraus representation
• A Fluctuation-Dissipation Structure of Quantum Dynamical Semigroups Reveals a Unique Internal Hamiltonian
• Some Quantum Dynamical Semi-groups with Quantum Stochastic Dilation