arXiv:1012.5653 · New Journal of Physics

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

André LeClair

Published May 25, 2011• 16 citations

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 η/ s >4.7 times the proposed lower bound of ℏ/4π k B , which came from the anti-Desitter space/conformal field theory correspondence (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 η/ s <1.3 times the bound.

DOI: 10.1088/1367-2630/13/5/055015

Related papers

S-matrix approach to quantum gases in the unitary limit: I. The two-dimensional case

Pye-Ton How, André LeClair

In three spatial dimensions, in the unitary limit of a non-relativistic quantum Bose or Fermi gas, the scattering length diverges. This occurs at a renormalization group fixed point. Thus these systems present interesting examples of interacting scale-invariant models with dynamical exponent z = 2. We study this problem in two and three spatial dimensions using the S -matrix-based approach to the thermodynamics we recently developed. It is well suited to the unitary limit where the S matrix S = − 1, since it allows an expansion in the inverse coupling. We define a meaningful scale-invariant, unitary limit in two spatial dimensions, where again the scattering length diverges. In the two-dimensional case, the integral equation for the pseudo-energy becomes transcendentally algebraic and we can easily compute the various universal scaling functions as a function of μ/ T , such as the energy per particle. The ratio of the shear viscosity to the entropy density η/ s is above the conjectured lower bound of for all cases except attractive bosons. For attractive two-component fermions, , whereas for attractive bosons .

arXiv:1001.1121Journal of Statistical Mechanics Theory and ExperimentMar 26, 20108 citations

S-matrix approach to quantum gases in the unitary limit: II. The three-dimensional case

Pye Ton How, André LeClair

A new analytic treatment of three-dimensional homogeneous Bose and Fermi gases in the unitary limit of negative infinite scattering length is presented, based on the S -matrix approach to statistical mechanics we recently developed. The unitary limit occurs at a fixed point of the renormalization group with dynamical exponent z = 2 where the S -matrix equals − 1. For fermions we find T c / T F ≈0.1. For bosons we present evidence that the gas does not collapse, but rather has a critical point that is a strongly interacting form of Bose–Einstein condensation. This bosonic critical point occurs at n λ T 3 ≈1.3, where n is the density and λ T the thermal wavelength, which is lower than the ideal gas value of ζ(3/2) = 2.61.

arXiv:1004.5390Journal of Statistical Mechanics Theory and ExperimentJul 1, 20109 citations

Viscosity bound violation in viscoelastic Fermi liquids

M P Gochan, Hua Li, K S Bedell

The anti-de Sitter/conformal field theory correspondence (AdS/CFT) has been used to determine a lower bound on the ratio of shear viscosity to entropy density ( s ) for strongly-coupled field theories with a gravity dual. The conjectured universal lower bound, given as , is a measure of interaction strength in a quantum fluid where equality indicates a perfect quantum fluid. In this paper we study η / s in a Fermi gas in the unitary limit. We show that in addition to a local minimum for η / s at which obeys the lower bound, a more interesting result exists in the violation of the η / s lower bound due to the superfluid fluctuations above T c . To conclude, we examine the viscoelastic properties of the unitary Fermi gas. Previous work brought to light the connection between violation of the η / s bound and a viscoelastic response in the context of holographic solids. We ultimately find that, in addition to holographic solids, all Fermi liquids with a viscoelastic response produced by superfluid fluctuations can violate the universal η / s lower bound.

arXiv:1801.08627Journal of Physics CommunicationsJun 1, 20198 citations

Quantum Bose and Fermi gases with large negative scattering length in the two-body S -matrix approximation

André LeClair, Edgar Marcelino de Carvalho Neto, André Nicolai +1 more

We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many-body processes that are reducible to two-body scatterings. This is done for arbitrary negative scattering length, which interpolates between the ideal and unitary gas limits. In the unitary limit, we compute the first four virial coefficients within our approximation. The second virial coefficient is exact, and we extend the previously known result for fermions to bosons and also for both bosons and fermions for the upper branch on the other side of unitarity (infinitely large positive scattering length). Assuming bosons can exist in a metastable state before undergoing mechanical collapse, we map out the critical temperatures for strongly coupled Bose-Einstein condensation as a function of scattering length.

arXiv:1205.0234Physical Review AAug 2, 20124 citations

Nearly perfect fluidity: from cold atomic gases to hot quark gluon plasmas

Thomas Schäfer, Derek A. Teaney

Shear viscosity is a measure of the amount of dissipation in a simple fluid. In kinetic theory shear viscosity is related to the rate of momentum transport by quasi-particles, and the uncertainty relation suggests that the ratio of shear viscosity η to entropy density s in units of ℏ/ k B is bounded by a constant. Here, ℏ is Planck's constant and k B is Boltzmann's constant. A specific bound has been proposed on the basis of string theory where, for a large class of theories, one can show that η/ s ⩾ ℏ/(4π k B ). We will refer to a fluid that saturates the string theory bound as a perfect fluid. In this review we summarize theoretical and experimental information on the properties of the three main classes of quantum fluids that are known to have values of η/ s that are smaller than ℏ/ k B . These fluids are strongly coupled Bose fluids, in particular liquid helium, strongly correlated ultracold Fermi gases and the quark gluon plasma. We discuss the main theoretical approaches to transport properties of these fluids: kinetic theory, numerical simulations based on linear response theory and holographic dualities. We also summarize the experimental situation, in particular with regard to the observation of hydrodynamic behavior in ultracold Fermi gases and the quark gluon plasma.

arXiv:0904.3107Reports on Progress in PhysicsNov 12, 2009437 citations

The S-Matrix Formulation Of Quantum Statistical Mechanics, With Applications To Cold Quantum Gas

Pye Ton How

A novel formalism of quantum statistical mechanics, based on the zero-temperature S-matrix of the quantum system, is presented in this thesis. In our new formalism, the lowest order approximation ("two-body approximation") corresponds to the exact resummation of all binary collision terms, and can be expressed as an integral equation reminiscent of the thermodynamic Bethe Ansatz (TBA). Two applications of this formalism are explored: the critical point of a weakly-interacting Bose gas in two dimensions, and the scaling behavior of quantum gases at the unitary limit in two and three spatial dimensions. We found that a weakly-interacting 2D Bose gas undergoes a superfluid transition at Tc [ALMOST EQUAL TO] 2[pi]n/[m log(2[pi]/mg )], where n is the number density, m the mass of a particle, and g the coupling. In the unitary limit where the coupling g diverges, the two-body kernel of our integral equation has simple forms in both two and three spatial dimensions, and we were able to solve the integral equation numerically. Various scaling functions in the unitary limit are defined (as functions of [MICRO SIGN]/T ) and computed from the numerical solutions. For bosons in three spatial dimensions, we present evidence that the gas undergoes 3 a strongly interacting version of Bose-Einstein condensation at n[lamda]T [ALMOST EQUAL TO] 1.3, where n is the number density and [lamda]T is the thermal wavelength. Finally, we look at the ratio of shear viscosity to entropy density [eta]/s of the unitary quantum gas, which has a conjectured lower bound of [eta]/s [GREATER-THAN OR EQUAL TO] /4[pi]kb based on the AdS/CFT correspondence of a strongly coupled Yang-Mills theory.

Aug 31, 20110 citations