Abstract:
Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of non-hydrodynamic modes. We review non-hydrodynamic modes in kinetic theory and gauge/gravity duality and discuss their signatures in trapped Fermi gases close to unitarity. Reanalyzing previously published experimental data, we find hints of non-hydrodynamic modes in cold Fermi gases in two and three dimensions.

Abstract:
Fermi gases with generalized Rashba spin orbit coupling inducedby a synthetic gauge field have the potential of realizing many interesting states such as rashbon condensates and topological phases. Here we develop a fluctuation theory of such systems and demonstrate that beyond-Gaussian effects are essential to capture the physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature ($T_c$) of a weakly attracting superfluid to the order of Fermi temperature, paving a pathway towards high $T_c$ superfluids.

Abstract:
The Hartree energy shift is calculated for a unitary Fermi gas. By including the momentum dependence of the scattering amplitude explicitly, the Hartree energy shift remains finite even at unitarity. Extending the theory also for spin-imbalanced systems allows calculation of polaron properties. The results are in good agreement with more involved theories and experiments.

Abstract:
We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase diagram where inhomogeneous phases are likely to exist. We show that an intriguing relation exists between the general structure of the many-body phase diagram and the binding energies of the underlying two-body bound-state problem, which further supports our findings. Our results suggest that inhomogeneous condensates form for mass ratios of the spin-down and spin-up fermions greater than three. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.

Abstract:
The maximal algebra of symmetries of the free single-particle Schroedinger equation is determined and its relevance for the holographic duality in non-relativistic Fermi systems is investigated. This algebra of symmetries is an infinite dimensional extension of the Schroedinger algebra, it is isomorphic to the Weyl algebra of quantum observables, and it may be interpreted as a non-relativistic higher-spin algebra. The associated infinite collection of Noether currents bilinear in the fermions are derived from their relativistic counterparts via a light-like dimensional reduction. The minimal coupling of these currents to background sources is rewritten in a compact way by making use of Weyl quantisation. Pushing forward the similarities with the holographic correspondence between the minimal higher-spin gravity and the critical O(N) model, a putative bulk dual of the unitary and the ideal Fermi gases is discussed.

Abstract:
We address recent spin transport experiments in ultracold unitary Fermi gases. We provide a theoretical understanding for how the measured temperature dependence of the spin diffusivity at low $T$ can disagree with the expected behavior of a Fermi liquid (FL) while the spin susceptiblity(following the experimental protocols) is consistent with a Fermi liquid picture. We show that the experimental protocols for extracting $\chi_s$ are based on a FL presumption; relaxing this leads to consistency within (but not proof of) a pseudogap-based approach. Our tranport calculations yield insight into the measured strong suppression of the spin diffusion constant at lower $T$.

Abstract:
We study the exact renormalisation group flow for ultracold Fermi-gases in unitary regime. We introduce a pairing field to describe the formation of the Cooper pairs, and take a simple ansatz for the effective action. Set of approximate flow equations for the effective couplings including boson and fermionic fluctuations is derived. At some value of the running scale, the system undergoes a phase transition to a gapped phase. The values of the energy density, chemical potential, pairing gap and the corresponding proportionality constants relating the interacting and non-interacting Fermi gases are calculated. Standard mean field results are recovered if we omit the boson loops.

Abstract:
The contact parameter in unitary Fermi Gases governs the short-distance, high-momentum, and high-energy properties of the system. We perform accurate quantum Monte Carlo calculations with highly optimized trial functions to precisely determine this parameter at T=0, demonstrate its universal application to a variety of observables, and determine the regions of momentum and energy over which the leading short-range behavior is dominant. We derive Tan's expressions for the contact parameter using just the short-range behavior of the ground-state many-body wave function, and use this behavior to calculate the two-body distribution function, one-body density matrix, and the momentum distribution of unitary Fermi gases; providing a precise value of the contact parameter that can be compared to experiments.

Abstract:
We study a dynamics of ultracold Fermi-gases near the unitary limit in the framework of Effective Field Theory. It is shown that, while one can obtain a reasonable description of the universal proportionality constant both in the narrow and the broad Feshbach resonance limits, the reguirement of the reparametrisation invariance leads to appearance of the three body forces needed to cancel the otherwise arising off-shell uncertainties. The size of the unsertainties is estimated.

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 eta/s > 4.7 times the proposed lower bound of \hbar/4 pi k_B which came from the 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 eta/s > 1.3 times the bound.