Strongly Interacting Fermi Gases: Hydrodynamics and Beyond

TL;DR

This thesis explores the out-of-equilibrium dynamics of strongly interacting Fermi gases using advanced hydrodynamics and gauge-gravity duality, aiming to better understand their fluidity and transport properties in relation to other quantum fluids.

Contribution

It introduces the use of second-order hydrodynamics and gauge-gravity duality to analyze collective modes and short-time dynamics in strongly interacting Fermi gases, revealing new non-hydrodynamic modes.

Findings

Higher-order collective modes are more sensitive probes of shear viscosity.

Predictions of non-hydrodynamic modes appear on short timescales where traditional hydrodynamics fails.

Strongly interacting Fermi gases nearly saturate the viscosity bound from AdS/CFT.

Abstract

This thesis considers out-of-equilibrium dynamics of strongly interacting non-relativistic Fermi gases in several two and three dimensional geometries. The tools of second-order hydrodynamics and gauge-gravity duality will be utilized to address this system. Many of the themes of this work are motivated by the observed similarities in transport properties between strongly interacting Fermi gases and other very different strongly interacting quantum fluids such as the quark-gluon plasma, high temperature superconductors, and quantum field theories described by gauge-gravity duality. In particular, these systems all nearly saturate the conjectured lower bound on the ratio of shear viscosity to entropy density $\eta/s \geq \hbar/(4 \pi k_B)$ coming from the AdS/CFT correspondence. Among other things, this observation, in conjunction with current experiment and data analysis in atomic, condensed matter, and nuclear physics lends itself to the following questions: How perfect of a fluid is the strongly interacting Fermi gas, and can one find a more stringent constraint on $\eta/s$ in Fermi gases? Do the similarities in transport properties among strongly interacting quantum systems extend beyond dynamics controlled by the hydrodynamical shear viscosity? In regards to the first question, by utilizing second-order hydrodynamics, it will be demonstrated that higher-order collective modes of a harmonically trapped Fermi gas may serve as a more sensitive probe of the shear viscosity. For the second question, both second-order hydrodynamics and a gravity dual theory are used to make predictions about dynamics occurring on short timescales where hydrodynamics is expected to break down. In particular the appearance of a class of "non-hydrodynamic" collective modes not contained within a Navier-Stokes description of the strongly interacting Fermi gas will be discussed.