Evolution of Bose–Einstein condensate systems beyond the Gross–Pitaevskii equation - Lyanda-Geller, Yuli (Frontiers in Physics, 2023)
While many phenomena in cold atoms and other Bose-Einstein condensate systems are often described using the mean field approaches, understanding the kinetics of Bose-Einstein condensates (BEC) requires the inclusion of particle scattering via the collision integral of the quantum Boltzmann equation. A rigorous approach to many problems in the dynamics of the BEC, such as the nucleation of the condensate or the decay of the persistent current, requires, in the presence of factors making a symmetry breaking possible, considering collisions with thermal atoms via the collision integral. These collisions permit the emergence of vorticity or other signatures of long-range order in the nucleation of the BEC or the transfer of angular momentum to thermal atoms in the decay of persistent current, due to corresponding terms in systems Hamiltonians. Here we also discuss the kinetics of spin-orbit coupled BEC. The kinetic equation for the particle spin density matrix is derived. Numerical simulations demonstrate significant effects of the collision integral on the dynamics of the spin-orbit coupled BEC upon quenching of the Raman coupling that generates synthetic electric and magnetic fields.