Scaling solutions of the two fluid hydrodynamic equations in a harmonically trapped gas at unitarity

Abstract

We prove that the two fluid Landau hydrodynamic equations, when applied to a gas interacting with infinite scattering length (unitary gas) in the presence of harmonic trapping, admit exact scaling solutions of mixed compressional and surface nature. These solutions are characterized by a linear dependence of the velocity field on the spatial coordinates and a temperature independent frequency which is calculated in terms of the parameters of the trap. Our results are derived in the regime of small amplitude oscillations and hold both below and above the superfluid phase transition. They apply to isotropic as well as to deformed configurations, thereby providing a generalization of Castin's theorem (Y. Castin, C. R. Phys. \textbf{5}, 407 (2004)) holding for isotropic trapping. Our predictions agree with the experimental findings in resonantly interacting atomic Fermi gases. The breathing scaling solution, in the presence of isotropic trapping, is also used to prove the vanishing of two bulk viscosity coefficients in the superfluid phase.

4 pages

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• Exploring the Thermodynamics of a Universal Fermi Gas
• Universal Thermodynamics of Degenerate Quantum Gases in the Unitarity Limit
• Precision Measurements of Collective Oscillations in the BEC-BCS Crossover
• Vanishing bulk viscosities and conformal invariance of unitary Fermi gas
• Thermodynamic Measurements in a Strongly Interacting Fermi Gas
• Collective oscillations of a trapped Fermi gas near a Feshbach resonance
• Collective Modes in a Unitary Fermi Gas across the Superfluid Phase Transition
• Collective excitations of a trapped degenerate Fermi gas
• Bose Gases Near Unitarity
• First and second sound in cylindrically trapped gases

Cited by in corpus (17)

• Observation of the Efimovian Expansion in Scale Invariant Fermi Gases
• Shear viscosity of a universal Fermi gas near the superfluid phase transition
• Observation of conformal symmetry breaking and scale invariance in expanding Fermi gases
• Anomalous minimum in the shear viscosity of a Fermi gas
• Bulk viscosity and contact correlations in attractive Fermi gases
• Collective oscillations of a trapped quantum gas in low dimensions
• First and second sound in a highly elongated Fermi gas at unitarity
• Measuring the Hydrodynamic Linear Response of a Unitary Fermi Gas
• Hydrodynamics with spacetime-dependent scattering length
• Hydrodynamic Relaxation in a Strongly Interacting Fermi Gas
• Observation of Dynamical Super Efimovian Expansion in a Unitary Fermi Gas
• Breathing mode frequency of a strongly interacting Fermi gas across the 2D-3D dimensional crossover
• First and second sound of a unitary Fermi gas in highly oblate harmonic traps
• Collective modes in the anisotropic unitary Fermi gas and the inclusion of a backflow term
• Universal Density Shift Coefficients for the Thermal Conductivity and Shear Viscosity of a Unitary Fermi Gas
• Dissipative superfluid hydrodynamics for the unitary Fermi gas
• First and second sound of a unitary Fermi gas in highly elongated harmonic traps