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Acta Physica Sinica

THEORY OF TWO-DIMENSIONAL FERMI LIQUIDS (Ⅲ)——TRA-NSPORT PROPERTIES AND SOUND PROPAGATION

Shi-Min Cui, CAI JIAN-HUA, (1)上海交通大学凝聚态物理研究所,上海,200030; (2)中国高等科学技术中心(世界实验室)理论物理分中心

Published Jan 1, 1990• 0 citations
Publisher

Abstract

We discuss transport properties and sound propagation of 2-D Fermi liquids. Microscopic expressions for the coefficients of diffusion, viscosity and thermal conductivity are derived using Resibois method. Velocities of the zeroth and first sounds are calculated. Based on an analysis of collision integral, it is shown that a series of relaxtion time parameters is necessary to define precisely the sound propagation properties in 2-D Fermi liquids, in contrast to the 3-D case.

DOI
10.7498/aps.39.580

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We discuss transport properties and sound propagation of 2-D Fermi liquids. Microscopic expressions for the coefficients of diffusion, viscosity and thermal conductivity are derived using Resibois method. Velocities of the zeroth and first sounds are calculated. Based on an analysis of collision integral, it is shown that a series of relaxtion time parameters is necessary to define precisely the sound propagation properties in 2-D Fermi liquids, in contrast to the 3-D case.
Strongly interacting two-dimensional Fermi systems are one of the great remaining challenges in many-body physics due to the interplay of strong local correlations and enhanced long-range fluctuations. Here, we probe the thermodynamic and transport properties of a 2D Fermi gas across the BEC-BCS crossover by studying the propagation and damping of sound modes. We excite particle currents by imprinting a phase step onto homogeneous Fermi gases trapped in a box potential and extract the speed of sound from the frequency of the resulting density oscillations. We measure the speed of sound across the BEC-BCS crossover and compare the resulting dynamic measurement of the equation of state both to a static measurement based on recording density profiles and to quantum Monte Carlo calculations and find reasonable agreement between all three. We also measure the damping of the sound mode, which is determined by the shear and bulk viscosities as well as the thermal conductivity of the gas. We find that the damping is minimal in the strongly interacting regime and the diffusivity approaches the universal quantum bound ℏ/m of a perfect fluid.
Transport coefficients of superfluid dipolar Fermi gas are calculated by using the Boltzmann equation approach. The interaction between Bogoliubov-Bogoliubov quasiparticles in the collision integral is considered in binary process. The shear viscosities nxz↑ = nyy↑,nxy↑; nxz↑ ≈ nyz↑; and nu↑ are proportional to T-6; T-8; and T-10 , respectively. Also, we have found the elements of the diffusive thermal conductivities Kxx↑= Kyy↑ with temperature dependency T-5 and Ku↑ which is proportional to T-7 and other components which are zero.
Abstract At low temperature, a normal gas of unpaired spin‐1/2 fermions is one of the cleanest realizations of a Fermi liquid. It is described by Landau's theory, where no phenomenological parameters are needed as the quasiparticle interaction function can be computed perturbatively in powers of the scattering length , the sole parameter of the short‐range interparticle interactions. Obtaining an accurate solution of the transport equation nevertheless requires a careful treatment of the collision kernel, as the uncontrolled error made by the relaxation time approximations increases when the temperature drops below the Fermi temperature. Here, sound waves in the hydrodynamic regime are studied up to second order in the Chapman‐Enskog's expansion. It is found that the frequency of the sound wave is shifted above its linear departure as where and are the speed and wavenumber of the sound wave and the typical collision time scales as . Besides the shear viscosity, the coefficient is described by a single second‐order collision time, which is computed exactly from an analytical solution of the transport equation, resulting in a positive dispersion . The results suggest that ultracold atomic Fermi gases are an ideal experimental system for quantitative tests of second‐order hydrodynamics.