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Derivation of non-Markovian transport equations for trapped cold atoms in nonequilibrium thermal field theory. (English) Zbl 1187.82091
The non-Markovian transport equations for the system of cold Bose atoms confined by an external potential both without and with a Bose-Einstein condensate are derived in the framework of nonequilibrium thermal field theory (thermo field dynamics). The key elements are an explicit particle representation and a self-consistent renormalization condition which are essential in thermal field theory. In order to make complicated calculations of self-energies transparent, the diagrammatic calculations in the tensor form are refined, and a convenient \(4\times4\)-matrix formulation in the condensed case is developed. The non-Markovian transport equation for the non-condensed system, derived at the two-loop level, is reduced in the Markovian limit to the ordinary quantum Boltzmann equation derived also by other methods. For the condensed system, it is obtained a new transport equation with an additional collision term which becomes important in the case of the Landau instability. The additional collision term represents the creation or annihilation of three quasiparticles, and prevents the system from equilibrating if a negative energy mode exists, and is suppressed otherwise. The transport equation derived in this paper can describe only the initial stage of the condensate decay with the Landau instability, and not the full time evolution of the decay process.

MSC:
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
82C70 Transport processes in time-dependent statistical mechanics
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
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