Dynamical Dipolar Condensate Finite Temperature Stochastic Gross--Pitaevskii--Boltzmann Model

We formulate a generalized self-consistent stochastic quantum kinetic theory for finite-temperature ultracold Bose gases interacting via a generic long-range interaction, applicable to a broad range of systems, by means of Keldysh non-equilibrium field theory: such model is explicitly cast in the context of dipolar atomic gases, and is also shown to encompass established stochastic and kinetic treatments for ultracold atomic gases with local interactions as special cases. The condensate and low-lying modes are collectively described by a stochastic Gross-Pitaevskii equation with two collisional terms and their corresponding stochastic noise terms, with thermal particles dynamically modelled through a self-consistently coupled Quantum Boltzmann equation and dipolar interactions included by means of a coupled Poisson-like equation. Additional use of Bogoliubov-de Gennes analysis generating the Lee-Huang-Yang correction term relevant in the $T=0$ quantum-fluctuation-dominated regime, allows us to postulate the extension of such model offering a plausible scheme for interpolating between quantum-dominated and thermal-dominated fluctuation regimes, the consistency of which remains to be tested against experimental observations.