Hydrodynamics with spacetime-dependent scattering length

Abstract

Hydrodynamics provides a concise but powerful description of long-time and long-distance physics of correlated systems out of thermodynamic equilibrium. Here we construct hydrodynamic equations for nonrelativistic particles with a spacetime-dependent scattering length and show that it enters constitutive relations uniquely so as to represent the fluid expansion and contraction in both normal and superfluid phases. As a consequence, we find that a leading dissipative correction to the contact density due to the spacetime-dependent scattering length is proportional to the bulk viscosity (${\zeta }_2$ in the superfluid phase). Also, when the scattering length is slowly varied over time in a uniform system, the entropy density is found to be produced even without fluid flows in proportion to the bulk viscosity, which may be useful as a novel probe to measure the bulk viscosity in ultracold-atom experiments.

9 pages, no figure; published version

References in corpus (17)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Ultracold atoms out of equilibrium
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Non-local density correlations as signal of Hawking radiation in BEC acoustic black holes
• Collective emission of matter-wave jets from driven Bose-Einstein condensates
• Collective excitation of a Bose-Einstein condensate by modulation of the atomic scattering length
• Ultracold Lattice Gases with Periodically Modulated Interactions
• Long-living Bloch oscillations of matter waves in optical lattices
• Apparent low-energy scale invariance in two-dimensional Fermi gases
• Universal properties of Fermi gases in arbitrary dimensions
• Large Amplitude Dynamics of the Pairing Correlations in a Unitary Fermi Gas
• Designer Spatial Control of Interactions in Ultracold Gases
• Scaling solutions of the two fluid hydrodynamic equations in a harmonically trapped gas at unitarity
• Association of Atoms into Universal Dimers using an Oscillating Magnetic Field

Cited by in corpus (20)

• High-temperature expansion of the viscosity in interacting quantum gases
• Bulk viscosity and contact correlations in attractive Fermi gases
• Viscosity spectral functions of resonating fermions in the quantum virial expansion
• Quantum critical thermal transport in the unitary Fermi gas
• Bulk viscosity of resonating fermions revisited: Kubo formula, sum rule, and the dimer and high-temperature limits
• Dynamics of strongly interacting Fermi gases with time-dependent interactions: Consequence of conformal symmetry
• Shear viscosity and Strong-Coupling Corrections in the BCS-BEC crossover Regime of an Ultracold Fermi Gas
• Simulating quantum transport with ultracold atoms and interaction effects
• Collisional dynamics of polaronic clouds immersed in a Fermi sea
• Hydrodynamic Attractor in Ultracold Atoms
• Thermal conductivity of a weakly interacting Bose gas in quasi-one-dimension
• Microscopic derivation of the Boltzmann equation for transport coefficients of resonating fermions at high temperature
• Bulk viscosity of dual Bose and Fermi gases in one dimension
• Bulk viscosity of resonantly interacting fermions in the quantum virial expansion
• Viscous Flow in a 1D Spin-Polarized Fermi Gas: the Role of Integrability on Viscosity
• Universal nonlinear responses of quantum Hall systems with Galilean invariance
• Hydrodynamic attractor in periodically driven ultracold quantum gases
• Viscous Drude weight of dual Bose and Fermi gases in one dimension
• Quantum transport in strongly correlated Fermi gases
• Dimer-projection contact and the clock shift of a unitary Fermi gas