On the viscosity to entropy density ratio for unitary Bose and Fermi Gases

Abstract

We calculate the ratio of the viscosity to the entropy density for both Bose and Fermi gases in the unitary limit using a new approach to the quantum statistical mechanics of gases based on the S-matrix. In the unitary limit the scattering length diverges and the S-matrix equals -1. For the fermion case we obtain eta/s > 4.7 times the proposed lower bound of \hbar/4 pi k_B which came from the AdS/CFT for gauge theories, consistent with the most recent experiments. For the bosonic case we present evidence that the gas undergoes a phase transition to a strongly interacting Bose-Einstein condensate, and is a more perfect fluid, with eta/s > 1.3 times the bound.

25 pages, 5 figures. v2: Minor addition on high T behavior; minor factors of 2 corrected, with no change in final result

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Cited by in corpus (11)

• Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
• Shear Viscosity of a Unitary Fermi Gas
• First and second sound in a highly elongated Fermi gas at unitarity
• Perfect-fluid behavior of a dilute Fermi gas near unitary
• Elliptic flow in a strongly-interacting normal Bose gas
• Shear viscosity and Strong-Coupling Corrections in the BCS-BEC crossover Regime of an Ultracold Fermi Gas
• Virial coefficients for Bose and Fermi trapped gases beyond the unitary limit: an S-Matrix approach
• Quantum Bose and Fermi gases with large negative scattering length in the 2-body S-matrix approximation
• Kovtun-Son-Starinets Conjecture and Effects of Mass Imbalance in the Normal State of an Ultracold Fermi Gas in the BCS-BEC Crossover Region
• Thermodynamics of the two-dimensional Hubbard model in the two-body scattering approximation
• Observation of Universal Expansion Anisotropy from Cold Atoms to Hot Quark-Gluon Plasma