Recent flurry of experiments on out-of-equilibrium dynamics in cold gases (Bosonic and Fermionic) has raised great interest in understanding collective behaviour of interacting particles. Although the dynamics of interacting gases depends on many details of the system, a great insight can be obtained in a rather universal limit of weak non-linearity, dispersion and dissipation. In this limit, using a reductive perturbation method we map many hydrodynamic models relevant to cold atoms to well known chiral one-dimensional equations such as Korteweg–de Vries (KdV), Burgers, KdV-Burgers, and Benjamin-Ono equations. This mapping of rather complicated hydrodynamic equations to known chiral one dimensional equations is of great experimental and theoretical interest. For instance, this mapping helps us to study the interplay between non-linearity, dissipation and dispersion which are the three hallmarks of nonlinear hydrodynamics all of which have been observed in experiments. This mapping is however expected to loose quantitative accuracy while comparing with certain experiments whose initial conditions, for instance, are very far out-of-equilibrium in which case one will need to solve the original hydrodynamic equations for a given setup. In this regard, I will describe another work in collaboration with the experimental group of John Thomas (Duke) on colliding clouds of strongly interacting Fermi-gas where we find near perfect quantitative agreement with experiment by solving the hydrodynamic equations for a Unitary Fermi gas. We provide the first evidence of shock waves (a fingerprint of nonlinear hydrodynamics) in this system of strongly interacting Fermi gas.
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