Relaxation processes in a condensed Bose gas

Erich D. Gust

A. L. Ivanov, Claudia Ell, H. Haug

The relaxation kinetics of an ideal Bose gas coupled to a phonon thermostat at temperature Tb below or equal to the critical temperature Tc consists of an initial transient and the following adiabatic stage. The transient depends on the initial distribution of bosons at t = 0 and lasts a few characteristic scattering times. The following nonexponential relaxation towards a quantum degenerate equilibrium state with a Bose-Einstein (BE) condensate is a slow adiabatic process. We find a generic solution of the phonon-assisted Boltzmann kinetics at the adiabatic stage. This solution is completely defined by the ratio Tc/Tb. Here, one has a unique example of the fundamental solution of Boltzmann kinetics that is insensitive to the initial distribution. For Tb → Tc from above, we develop a theory of the thermodynamic critical slowing-down which also leads to the nonexponential thermalization of bosons. We apply our results to the relaxation kinetics of para-excitons in Cu2O and reinterpret the recent reports on the observation of BE condensation of para-excitons.

Miguel Escobedo, Federica Pezzotti, Manuel A. Valle

Shingo Otsuka

P. Stenius, Wei-Juan Zhao, Ataç İmamoğlu

We study the condensation of a two-dimensional exciton gas in a harmonic trap using a quantum Boltzmann equation. The excitons interact with a lattice that is kept at a constant temperature and we also include exciton–photon coupling (dissipation) and exciton–exciton interactions. We compare the condensation time for both an interacting and a non-interacting exciton gas. For a non-interacting gas anti-Stokes type processes dominate the relaxation rate of low-energy states. The condensation time-scale is determined by the (phonon) scattering rate into the ground state. The presence of dissipation results in a heating effect which increases the mean number of Bose particles required for the onset of condensation. For a dissipative gas the steady state is a nonequilibrium condensate (exciton matter laser), where the exciton temperature remains above the lattice temperature. We also discuss the effects of dimensionality and trapping on the relaxation process, which has a fundamental role in establishing the condensation time-scale.

G. M. Kavoulakis, C. J. Pethick, H. Smith

We present a unified account of damping of low-lying collective modes and of relaxation of temperature anisotropies in a trapped Bose gas in the collisionless regime. By means of variational techniques, we show that the relaxation times for the two situations are closely related to the simplest variational estimate of the viscous relaxation time. We derive rather precise theoretical expressions for the characteristic relaxation times and compare our results with experiment.