Strongly Interacting Fermi Gases: Hydrodynamics and Beyond

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 $\eta /s\ge \hslash /(4\pi k_B)$ 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.

arXiv commentThesis 121 pages, 31 figures, 3 appendeces

References in corpus (40)

• Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• New Developments in Relativistic Viscous Hydrodynamics
• Spin-Imbalance in a One-Dimensional Fermi Gas
• Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas
• New theories of relativistic hydrodynamics in the LHC era
• Universal Quantum Viscosity in a Unitary Fermi Gas
• Higher flow harmonics from (3+1)D event-by-event viscous hydrodynamics
• Homogeneous Atomic Fermi Gases
• Quasinormal Modes of Near Extremal Black Branes
• Observation of a pairing pseudogap in a two-dimensional Fermi gas
• Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
• Expansion of an interacting Fermi gas
• Lifshitz holography
• Scale invariance and viscosity of a two-dimensional Fermi gas
• Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade
• Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit
• The Shear Viscosity to Entropy Density Ratio of Trapped Fermions in the Unitarity Limit
• Shear viscosity and damping for a Fermi gas in the unitarity limit
• Finite-Temperature Collective Dynamics of a Fermi Gas in the BEC-BCS Crossover
• Hydrodynamic Expansion of a Strongly Interacting Fermi-Fermi Mixture
• Apparent low-energy scale invariance in two-dimensional Fermi gases
• Dynamics of a strongly interacting Fermi gas: the radial quadrupole mode
• Anomalous minimum in the shear viscosity of a Fermi gas
• Frequency and damping of the Scissors Mode of a Fermi gas
• Shear Viscosity of a Unitary Fermi Gas
• Model-independent determination of the shear viscosity of a trapped unitary Fermi gas: Application to high temperature data
• Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics
• Non-hydrodynamic transport in trapped unitary Fermi gases
• Collective oscillations of a trapped quantum gas in low dimensions
• Shear viscosity and damping of collective modes in a two-dimensional Fermi gas
• Collective modes of a two-dimensional spin-1/2 Fermi gas in a harmonic trap
• Towards a gravity dual of the unitary Fermi gas
• On a scale-invariant Fermi gas in a time-dependent harmonic potential
• Lattice Boltzmann simulations of a two-dimensional Fermi gas at unitarity
• String-Theory-Based Predictions for Nonhydrodynamic Collective Modes in Strongly Interacting Fermi Gases
• Lattice Boltzmann method for bosons and fermions and the fourth order Hermite polynomial expansion
• On the Quantization of the Monoatomic Ideal Gas
• Radial quadrupole and scissors modes in trapped Fermi gases across the BCS phase transition
• Higher-Harmonic Collective Modes in a Trapped Gas from Second-Order Hydrodynamics