Quantum dynamical semigroups for diffusion models with Hartree interaction

DOI10.1007/s00220-004-1172-xzbMath1085.82004arXivmath-ph/0309052OpenAlexW2061003687MaRDI QIDQ816043

Anton Arnold, Christof Sparber

Publication date: 20 February 2006

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0309052

zbMATH Keywords

open quantum systemmean-field approximationLindblad equationquantum Fokker-Planckquantum-dynamical semigroups

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Applications of operator theory in the physical sciences (47N50) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10)

Related Items

The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive effects, Regularity of solutions to quantum master equations: A stochastic approach, Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction, The Wigner(–Poisson)–Fokker–Planck equation with singular potential, REMARKS ON SUFFICIENT CONDITIONS FOR CONSERVATIVITY OF MINIMAL QUANTUM DYNAMICAL SEMIGROUPS, THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR, Quantum transport and Boltzmann operators, Diffusive corrections to asymptotics of a strong-field quantum transport equation, Convergence rates for quantum evolution and entropic continuity bounds in infinite dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Vlasov dynamics and its fluctuations in the \(1/N\) limit of interacting classical particles
• Semigroups of linear operators and applications to partial differential equations
• Nonlinear quantum dynamical semigroups for many-body open systems
• Path integral approach to quantum Brownian motion
• The Fokker-Planck equation. Methods of solution and applications.
• An existence proof for the Hartree-Fock time-dependent problem with bounded two-body interaction
• On the generators of quantum dynamical semigroups
• Brownian motion of a quantum harmonic oscillator
• Quantum dynamical semigroups and the neutron diffusion equation
• On Wigner measures
• Sufficient conditions for conservativity of quantum dynamical semigroups
• Quantum moment hydrodynamics and the entropy principle
• Fokker-Planck equations as scaling limits of reversible quantum systems
• An analysis of quantum Fokker-Planck models: a Wigner function approach
• Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions
• On the periodic Wigner--Poisson--Fokker--Planck system
• Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
• \(N\)-particle approximation to the nonlinear Vlasov-Poisson system.
• On the long-time behavior of the quantum Fokker-Planck equation
• Translation-covariant Markovian master equation for a test particle in a quantum fluid
• Quantum Dynamical Systems
• Steady states in plasma physics—the Vlasov-Fokker-Planck equation
• Quantum coding theorems
• Quantum optical versus quantum Brownian motion master equation in terms of covariance and equilibrium properties
• Self-consistent relaxation-time models in quantum mechanics
• Positive Functions on C ∗ -Algebras
• Quantum noise. A handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics.