Global \(L^{1}\) theory and regularity for the 3D nonlinear Wigner-Poisson-Fokker-Planck system.

DOI10.1016/j.jde.2003.07.004zbMath1039.35093OpenAlexW2063879186MaRDI QIDQ1428641

José A. Cañizo, Juanjo Nieto, José Luis López

Publication date: 29 March 2004

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2003.07.004

zbMATH Keywords

regularityexistenceglobal solutionWigner equationquantum diffusionopen quantum systemelliptic regularizationHusimi transformFokker-Planck operatorunqiueness

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Transport processes in time-dependent statistical mechanics (82C70)

Related Items (13)

The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive effects ⋮ On global solutions to some non-Markovian quantum kinetic models of Fokker-Planck type ⋮ Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation ⋮ The Wigner(–Poisson)–Fokker–Planck equation with singular potential ⋮ THE MODIFIED QUANTUM WIGNER SYSTEM IN WEIGHTED -SPACE ⋮ THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR ⋮ Quantum transport and Boltzmann operators ⋮ An analysis of quantum Fokker-Planck models: a Wigner function approach ⋮ On a rigorous interpretation of the quantum Schrödinger-Langevin operator in bounded domains with applications ⋮ On the Cauchy problem for Wigner-Poisson-BGK equation in the Wiener algebra ⋮ A hydrodynamic approach to multidimensional dissipation-based Schrödinger models from quantum Fokker-Planck dynamics ⋮ On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions ⋮ Global solutions of the mean–field, very high temperature Caldeira–Leggett master equation

Cites Work

• Unnamed Item
• Unnamed Item
• Semigroups of linear operators and applications to partial differential equations
• Path integral approach to quantum Brownian motion
• On the generators of quantum dynamical semigroups
• On Wigner measures
• Exponential decay in time of solutions of the viscous quantum hydrodynamic equations
• Fokker-Planck equations as scaling limits of reversible quantum systems
• An analysis of quantum Fokker-Planck models: a Wigner function approach
• Asymptotic behaviour and selfsimilarity for the three dimensional Vlasov-Poisson-Fokker-Planck system
• Regular solutions of the Vlasov-Poisson-Fokker-Planck system.
• Smoothing effect for the nonlinear Vlasov-Poisson-Fokker-Planck system
• Decoherent Histories and Quantum State Diffusion

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