Non-equilibrium dynamical modelling
Joint Quantum Centre (JQC) Durham-Newcastle, Newcastle University, UK
Atomtronic devices and envisaged applications rely on the coherent dynamics of the ultracold atomic matter-wave field, and its rapid generation from a thermal vapour by crossing the Bose-Einstein condensation phase transition. Nonetheless, the presence of incoherent processes, fluctuations and dissipation often require modelling beyond the simple mean field limit. Starting with a brief review of the Gross-Pitaevskii equation, these lectures discuss key approaches addressing such issues by extending the Gross-Pitaevskii equation through its self-consistent coupling to a dynamical thermal cloud, and the incorporation of fluctuations. Applications of these kinetic/stochastic methods to dissipative supercurrent and vortex dynamics, shot-to-shot fluctuations and phase transition crossing will be discussed, alongside the role these play in ring-trap geometries.