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arXiv:cond-mat/0104463

Microscopic Evolution of a Weakly Interacting Homogeneous Bose Gas

Daniel Gustavo Barci, Eduardo Souza Fraga, Rudnei O. Ramos

Published Apr 24, 2001• 6 citations
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Abstract

We provide a detailed description of the nonequilibrium time evolution of an interacting homogeneous Bose-Einstein condensate. We use a nonperturbative in-medium quantum field theory approach as a microscopic model for the Bose gas. The real-time dynamics of the condensate is encoded in a set of self-consistent equations which corresponds to an infinite sum of ladder Feynman diagrams. The crucial role played by the interaction between fluctuations for the instability generation is thoroughly described.

DOI
10.48550/arxiv.cond-mat/0104463

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We provide a detailed description of the nonequilibrium time evolution of an interacting homogeneous Bose-Einstein condensate. We use a nonperturbative in-medium quantum field theory approach as a microscopic model for the Bose gas. The real-time dynamics of the condensate is encoded in a set of self-consistent equations which corresponds to an infinite sum of ladder Feynman diagrams. The crucial role played by the interaction between fluctuations for the instability generation is thoroughly described.
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A dynamical many-body theory is presented which systematically extends beyond mean-field and perturbative quantum-field theoretical procedures. It allows us to study the dynamics of strongly interacting quantum-degenerate atomic gases. The nonperturbative approximation scheme is based on a systematic expansion of the two-particle irreducible effective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory, and ``off-shell'' effects that are not captured by the Gross-Pitaevskii equation. This is relevant to account for the dynamics of, e.g., strongly interacting quantum gases atoms near a scattering resonance, or of one-dimensional Bose gases in the Tonks-Girardeau regime. We apply the theory to a homogeneous ultracold Bose gas in one spatial dimension. Considering the time evolution of an initial state far from equilibrium we show that it quickly evolves to a nonequilibrium quasistationary state and discuss the possibility to attribute an effective temperature to it. The approach to thermal equilibrium is found to be extremely slow.
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The kinetics of the formation of coherent correlation properties associated with Bose condensation is studied in detail. The evolution of a nonequilibrium state with no “condensate-seed” is related to a hierarchy of relaxation times. At the first stage, a particle flux in energy space toward low energies sets in. The evolution in this case is described by a nonlinear Boltzmann equation, with a characteristic time given by interparticle collisions. When the particles which will later form the condensate have a kinetic energy which is less than the potential energy, a quasicondensate starts to form. In this stage, fluctuations of the density (but not of the phase) are suppressed and short-range coherent correlation properties are governed by the equation of motion for a quasiclassical complex field. The next stage is connected with the formation of the long-range order. The time for forming topological order and therefore genuine superfluidity proves to be dependent on the system size. The off-diagonal long-range order, arising after the attenuation of long-wave phase fluctuations, has a size-dependent relaxation time as well. Introduction The problem of Bose–Einstein Condensation (BEC) kinetics, being interesting in itself, has acquired a special significance in connection with experimental efforts to observe this condensation in a number of systems with particles with a finite lifetime. Such systems include spin-polarized atomic hydrogen [1], excitons [2] and biexcitons [3] in semiconductors and, more recently, laser-cooled atomic systems [4].