The evolution of quantum gases, released from traps, is studied through hydrodynamics, both analytically and numerically, in one and two dimensions. In particular, we demonstrate the existence of long time self-similar solutions of the Euler equations, for the density and velocity fields, and derive the scaling exponents as well as the scaling functions. We find that the expanding gas develops a shock-like front and the size of the cloud grows in time as a power law. We relate the associated exponent to that appearing in the corresponding equation of state of the quantum gas. Furthermore, we study the relaxation dynamics of a trapped quantum gas and show that the resulting steady state is in excellent agreement with that derived analytically. Our hydrodynamic approach is versatile and can be used to unravel several other far-from-equilibrium collective phenomenon of extreme nature, relevant to the growing experimental interests in quantum gases.

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• Cold and ultracold molecules
• Cold atoms & matter waves
• Compressible flows
• Equations of state
• Fermi gases
• Shock waves
• Direct numerical simulations
• Euler equation
• Hydrodynamic models
• Semiclassical physics
• Statistical hydrodynamics