Viscosity and scale invariance in the unitary Fermi gas

Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.10.002· OSTI ID:21579859

Enss, Tilman ^[1]; Haussmann, Rudolf ^[2]; Zwerger, Wilhelm ^[1]

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1. Technische Universitaet Muenchen, James-Franck-Strasse, D-85747 Garching (Germany)
2. Fachbereich Physik, Universitaet Konstanz, D-78457 Konstanz (Germany)

We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions are shown to be crucial to reproduce the full Boltzmann equation result in the high-temperature, low fugacity limit. The frequency dependent shear viscosity {eta}({omega}) exhibits a Drude-like transport peak and a power-law tail at large frequencies which is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium pressure, in agreement with a sum rule due to Taylor and Randeria. Near the superfluid transition the peak width is of the order of 0.5T{sub F}, thus invalidating a quasiparticle description. The ratio {eta}/s between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound h/(4{pi}k{sub B}) by a factor of about seven.

• OSTI ID: 21579859
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 3; Other Information: DOI: 10.1016/j.aop.2010.10.002; PII: S0003-4916(10)00179-X; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOLTZMANN EQUATION
CORRECTIONS
DENSITY
ENTROPY
EQUILIBRIUM
FERMI GAS
FREQUENCY DEPENDENCE
KUBO FORMULA
OMEGA BARYONS
SCALE INVARIANCE
STRING MODELS
STRING THEORY
SUM RULES
SUPERFLUIDITY
TANTALUM NITRIDES
TRANSITION TEMPERATURE
VISCOSITY
WARD IDENTITY
BARYONS
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
EXTENDED PARTICLE MODEL
FERMIONS
HADRONS
HYPERONS
INTEGRO-DIFFERENTIAL EQUATIONS
INVARIANCE PRINCIPLES
KINETIC EQUATIONS
MATHEMATICAL MODELS
M-THEORY
NITRIDES
NITROGEN COMPOUNDS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PHYSICAL PROPERTIES
PNICTIDES
QUARK MODEL
REFRACTORY METAL COMPOUNDS
STRANGE PARTICLES
TANTALUM COMPOUNDS
THERMODYNAMIC PROPERTIES
TRANSITION ELEMENT COMPOUNDS