Nonlinear quantum dynamical semigroups for many-body open systems
type: Item
instance of: scholarly article
title: Nonlinear quantum dynamical semigroups for many-body open systems
zbMATH Open document ID: 0584.35054
DOI: 10.1007/BF01012712
author: B. George
published in: Journal of Statistical Physics
publication date: 1983-01-01T00:00:00Z
review text: The notion of a nonlinear quantum dynamical semigroup is introduced, and the existence and uniqueness of solutions of the corresponding nonlinear evolution equations are studied in a more abstract framework. The construction of nonlinear quantum dynamical semigroups is carried out for two different mean-field models. First a mean-field coupling between a system of noninteracting subsystems and the bath is investigated. As examples, a nonlinear frictional Schrödinger equation and a model for a quantum Boltzmann equation are discussed. Second, a many-body system with mean-field interaction coupled to a bath is considered. Here, again, the form of the generator is derived; however, it cannot be obtained rigorously, except for some particular examples. Finally, the quantum Ising-Weiss model is briefly studied.
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 81U10
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 3935598
zbMATH Keywords: nonlinear quantum dynamical semigroup
zbMATH Keywords: nonlinear evolution equations
zbMATH Keywords: mean-field models
zbMATH Keywords: frictional Schrödinger equation
zbMATH Keywords: quantum Boltzmann equation
zbMATH Keywords: many-body system with mean-field interaction
MaRDI profile type: Publication
cites work: A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
cites work: Q5571997
cites work: On the generators of quantum dynamical semigroups
cites work: Properties of quantum Markovian master equations
cites work: Q4066072
cites work: Q5653193
cites work: Symmetric states of infinite tensor products of \(C^ *\)-algebras
cites work: Locally normal symmetric states and an analogue of de Finetti's theorem
cites work: Markovian master equations
cites work: Markovian master equations. II
cites work: Entropy production for quantum dynamical semigroups
cites work: Quantum dynamical semigroups and approach to equilibrium
cites work: An algebraic condition for the approach to equilibrium of an open N-level system
cites work: Equilibrium states for mean field models
description: scientific article; zbMATH DE number 3935598