A Doob h-transform of the Gross-Pitaevskii Hamiltonian

DOI10.1007/s10955-015-1337-3zbMath1327.82062OpenAlexW1083940473MaRDI QIDQ892419

Stefania Ugolini, Sergio A. Albeverio

Publication date: 19 November 2015

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-015-1337-3

zbMATH Keywords

Bose-Einstein condensationquasi-stationary distributionstochastic mechanicsdiffusions with KillingGross-Pitaevskii scaling limitinteracting Nelson diffusions

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stopping times; optimal stopping problems; gambling theory (60G40) Diffusion processes (60J60) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic mechanics (including stochastic electrodynamics) (81P20) Stochastic quantization (81S20)

Related Items (5)

Entropy chaos and Bose-Einstein condensation ⋮ Some Connections Between Stochastic Mechanics, Optimal Control, and Nonlinear Schrödinger Equations ⋮ Strong Kac’s chaos in the mean-field Bose–Einstein Condensation ⋮ Non-local Markovian symmetric forms on infinite dimensional spaces. I: The closability and quasi-regularity ⋮ McKean Feynman-Kac probabilistic representations of non-linear partial differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The mathematics of the Bose gas and its condensation.
• Stochastic description of a Bose-Einstein condensate
• Quasilimiting behavior for one-dimensional diffusions with killing
• Conservative diffusions
• Derivation of the Gross-Pitaevskii equation for rotating Bose gases
• Theory and applications of stochastic processes. An analytical approach
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Non-symmetric diffusions and related Hamiltonians
• One-dimensional behavior of dilute, trapped Bose gases
• Stability of regime-switching stochastic differential equations
• Rigorous derivation of the cubic NLS in dimension one
• Quasistationary distributions for one-dimensional diffusions with killing
• Role of scaling limits in the rigorous analysis of Bose-Einstein condensation
• Energy forms, Hamiltonians, and distorted Brownian paths
• ERGODIC PRORERTY OF N-DIMENSIONAL RECURRENT MARKOV PROCESSES
• Localization of Relative Entropy in Bose–Einstein Condensation of Trapped Interacting Bosons
• Stochastic quantization for a system ofNidentical interacting Bose particles
• An introduction to continuous-time stochastic processes. Theory, models, and applications to finance, biology, and medicine.
• The kinetic and interaction energies of a trapped Bose gas: beyond the mean field

This page was built for publication: A Doob h-transform of the Gross-Pitaevskii Hamiltonian