The anti-de Sitter/conformal field theory correspondence (AdS/CFT) has been used to determine a lower bound on the ratio of shear viscosity h ( )to entropy density (s) for strongly-coupled field theories with a gravity dual. The conjectured universal lower bound, given as s k 4 B   h p , 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 T T 2 c » 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.

Using the Landau kinetic equation to study the non-equilibrium behavior of interacting Fermi systems is one of the crowning achievements of Landau's Fermi liquid theory. While thorough study of transport modes has been done for standard three-dimensional Fermi liquids, an equally in-depth analysis for two dimensional Fermi liquids is lacking. In applying the Landau kinetic equation (LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of the zero sound mode c 0 . As a function of the usual dimensionless parameter s = ω/qv F , we find two peculiar results: First, for |s| > 1 we see the propagation of an undamped mode for weakly interacting systems. This differs from the three dimensional case where an undamped mode only propagates for repulsive interactions and the mode experiences Landau damping for any arbitrary attractive interaction. Second, we find that regardless of interaction strength, a propagating mode is forbidden for |s| < 1. This is profoundly different from the three-dimensional case where a mode can propagate, albeit damped. In addition, we present a revised Pomeranchuk instability condition for a two-dimensional Fermi liquid as well as equations of motion for the fluid that follow directly from the LKE. In two dimensions, we find a constant minimum for all Landau parameters for l ≥ 1 which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency ω p exhibiting a crossover to the zero sound mode.

Dirac materials are systems in which the dispersion is linear in the vicinity of the Dirac points. As a consequence of this linear dispersion, the Fermi velocity is independent of density and these systems exhibit unusual behavior and possess unique physical properties that are of considerable interest. In this work we study the ground state behavior of 1D Dirac materials in two ways. First, using the Virial Theorem, we find agreement with a previous result in regards to the total average ground state energy. Namely, that the total average ground state energy, regardless of dimensionality, is found to be E = B/r s where B is a constant independent of r s . As a consequence, thermodynamic results as well as the characteristic exponents of 1D Fermi systems are density independent. Second, using conventional techniques, i.e. Tomanaga Luttinger theory (TLL), we find several unique properties that are a direct consequence of the dispersion. Specifically, the collective modes of the system exhibit electron density independence predicted from the Virial Theorem. Finally, experimental techniques are discussed in which these predictions of density independent exponents and their behavior can be tested.Recent angle resolved photoemission spectroscopy (ARPES) measurements performed on SWNTs have exposed behavior consistent with TLL theory [10].

We study the intrinsic effects of dimensional reduction on the transport equation of a perfectly two-dimensional Landau-Fermi liquid. By employing the orthogonality condition on the 2D analog of the Fourier-Legendre expansion, we find that the equilibrium and non-equilibrium properties of the fermionic system differ from its three-dimensional counterpart, with the latter changing drastically. Specifically, the modified Landau-Silin kinetic equation is heavily dependent on the solution of a nontrivial contour integral specific to the 2D liquid. We find the solution to this integral and its generalizations, effectively reducing the problem of solving for the collective excitations of a collisonless two-dimensional Landau-Fermi liquid to solving for the roots of some high-degree polynomial. This analysis ultimately lays the mathematical foundation for the exploration of atypical behavior in the non-equilibrium properties of two-dimensional fermionic liquids in the context of the Landau quasiparticle paradigm.