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The experimental realization of stable, ultracold Fermi gases near a Feshbach resonance allows to study gases with attractive interactions of essentially arbitrary strength. They extend the classic paradigm of BCS into a regime which has never been accessible before. We review the theoretical concepts which have been developed in this context, including the Tan relations and the notion of fixed points at zero density, which are at the origin of universality. We discuss in detail the universal thermodynamics of the unitary Fermi gas which allows a fit free comparison between theory and experiment for this strongly interacting system. In addition, we adress the consequences of scale invariance at infinite scattering length and the subtle violation of scale invariance in two dimensions. Finally we discuss the Fermionic excitation spectrum accessible in momentum resolved RF-spectroscopy and the origin of universal lower bounds for the shear viscosity and the spin diffusion constant.
We derive the phonon damping rate due to the four-phonon Landau-Khalatnikov process in low temperature strongly interacting Fermi gases using quantum hydrodynamics, correcting and extending the original calculation of Landau and Khalatnikov [ZhETF, 1
We analytically determine the properties of three interacting fermions in a harmonic trap subject to an external rotation. Thermodynamic quantities such as the entropy and energy are calculated from the third order quantum virial expansion. By parame
We present an experimental investigation of collective oscillations in harmonically trapped Fermi gases through the crossover from two to three dimensions. Specifically, we measure the frequency of the radial monopole or breathing mode as a function
We prepare and study strongly interacting two-dimensional Bose gases in the superfluid, the classical Berezinskii-Kosterlitz-Thouless (BKT) transition, and the vacuum-to-superfluid quantum critical regimes. A wide range of the two-body interaction st
We analytically determine the properties of two interacting particles in a harmonic trap subject to a rotation or a uniform synthetic magnetic field, where the spherical symmetry of the relative Hamiltonian is preserved. Thermodynamic quantities such