Transport coefficients from the boson Uehling-Uhlenbeck equation

Abstract

We derive microscopic expressions for the bulk viscosity, shear viscosity and thermal conductivity of a quantum degenerate Bose gas above TC , the critical temperature for Bose-Einstein condensation. The gas interacts via a contact potential and is described by the Uehling-Uhlenbeck equation. To derive the transport coefficients, we use Rayleigh-Schrodinger perturbation theory rather than the Chapman-Enskog approach. This approach illuminates the link between transport coefficients and eigenvalues of the collision operator. We find that a method of summing the second order contributions using the fact that the relaxation rates have a known limit improves the accuracy of the computations. We numerically compute the shear viscosity and thermal conductivity for any boson gas that interacts via a contact potential. We find that the bulk viscosity remains identically zero as it is for the classical case.

On the dynamics of finite temperature trapped Bose gases

“…Note that in this temperature regime, the transition probability is K 22 = 1 (cf. [47,49]), which is different from the regime considered in this paper. The existence of a global weak and measure solution for the equation was treated in [59,60,61].…”

“…Such toy models are indeed useful and have been used in the physics community (cf. [29,47,48,49]), under the assumption that the temperature of the system is very low T < 0.01T BEC . In such a low temperature system, the portion of excited atoms outside the condensate is very small, in comparison with the number of condensed atoms; and therefore N c can be regarded as a constant.…”

“…Indeed, the contribution of [48] is that they could derive a new collision operator C 13 [f ] which complements the ZNG theory in some cases. We refer to [47,48,49] for the discussion about the reason why the number of the excitations (bogolon number) is not conserved. In those works, the solutions of the kinetic equations are shown to converge to equilibrium and explicit convergence rates are computed.…”

Fast and accurate calculation of dilute quantum gas using Uehling–Uhlenbeck model equation

“…Gust and Reichl [22] calculated transport coefficients for the hard sphere (HS) molecule (ξ = 1 in Eq. ( 3)) using Rayleigh-Schrödinger perturbation theory rather than the kinetic calculation on the basis of Chapman-Enskog method [23].…”

First and second sounds in a degenerate Bose gas

“…This determinant can be evaluated using the method of successive approximations. This approach can be quite convenient and fruitful tool for the theoretical description of weakly nonequilibrium processes [9].…”