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arXiv:cond-mat/9908043

Kinetic Theory of Collective Modes in Atomic Clouds above the Bose-Einstein Transition Temperature

Usama Al Khawaja, C. J. Pethick, H. Smith

Published Aug 3, 1999• 0 citations
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Abstract

We calculate frequencies and damping rates of the lowest collective modes of a dilute Bose gas confined in an anisotropic trapping potential above the Bose-Einstein transition temperature. From the Boltzmann equation with a simplified collision integral we derive a general dispersion relation that interpolates between the collisionless and hydrodynamic regimes. In the case of axially symmetric traps we obtain explicit expressions for the frequencies and damping rates of the lowest modes in terms of a phenomenological collision time. Our results are compared with microscopic calculations and experiments.

DOI
10.48550/arxiv.cond-mat/9908043

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We discuss the collective modes of a trapped Bose gas in the hydrodynamic regime where atomic collisions ensure local thermal equilibrium for the distribution function. Starting from the conservation laws, in the linearized limit we derive a closed equation for the velocity fluctuations in a trapped Bose gas above the Bose-Einstein transition temperature. Explicit solutions for a parabolic trap are given. We find that the surface modes above the transition have the same dispersion relation as the one recently obtained by Stringari for the oscillations of the condensate at T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 within the Thomas-Fermi approximation. Results are also given for the monopole ``breathing'' mode as well as for the m=0m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0m=0 excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well.
In Chapter 17, we derived the Landau–Khalatnikov two-fluid hydrodynamics which describes the collision-dominated region of a trapped Bose condensate interacting with a thermal cloud. In this chapter, we use these equations to discuss the damping of the hydrodynamic collective modes in a trapped Bose gas at finite temperatures. We derive variational expressions based on these equations for both the frequency and the damping of collective modes. This extends the analysis in Chapter 16 in which a variational approach was developed to calculate the hydrodynamic two-fluid oscillation frequencies in the non-dissipative limit. A novel feature of our treatment is the introduction of frequency-dependent transport coefficients, which produce a natural cutoff eliminating the collisionless region in the low-density tail of the thermal cloud. Our expression for the damping in trapped superfluid Bose gases is a natural generalization of the approach used by Landau and Lifshitz (1959) for uniform classical fluids. This chapter is mainly based on Nikuni and Griffin (2004). In Chapters 15 and 17, we derived a closed set of two-fluid hydrodynamic equations for a trapped Bose-condensed gas starting from the simplified microscopic model describing the coupled dynamics of the condensate and noncondensate atoms given in Chapter 3. These hydrodynamic two-fluid equations include dissipative terms associated with the shear viscosity, the thermal conductivity and the four second viscosity coefficients. Explicit formulas for these transport coefficients were derived in Section 18.1. Our goal in this chapter is to find a general expression for the damping of the two-fluid modes in terms of these transport coefficients. We emphasize that the damping of hydrodynamic two-fluid oscillations is completely different in nature from the Landau and Beliaev damping of oscillations in the collisionless region which is treated in Chapters 12 and 13.