Collective mode damping and viscosity in a 1D unitary Fermi gas

Abstract

We calculate the damping of the Bogoliubov-Anderson mode in a one-dimensional two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-Ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther-Emery liquid of weakly bound pairs to a Lieb-Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks-Girardeau gas with a universal constant ${\alpha }_{\zeta }=0.38$ in the viscosity $\zeta ={\alpha }_{\zeta }\hslash n$ for T=0. For the trapped case, we calculate the Q-factor of the breathing mode and show that the damping provides a sensitive measure of temperature in 1D Fermi gases.

arXiv comment9 pages, 3 figures, published version (minor changes)

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• Many-Body Physics with Ultracold Gases
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Viscosity and scale invariance in the unitary Fermi gas
• Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
• Non-Equilibrium Universality in the Heating Dynamics of Interacting Luttinger Liquids
• Prethermalization and Thermalization of a Quenched Interacting Luttinger Liquid
• Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation
• Quantum phase diagrams of fermionic dipolar gases for an arbitrary orientation of dipole moment in a planar array of 1D tubes
• Kinetic Theory for Interacting Luttinger Liquids
• Thermalization Dynamics of Two Correlated Bosonic Quantum Wires After a Split
• Shear viscosity and Strong-Coupling Corrections in the BCS-BEC crossover Regime of an Ultracold Fermi Gas
• Viscous Flow in a 1D Spin-Polarized Fermi Gas: the Role of Integrability on Viscosity
• Kovtun-Son-Starinets Conjecture and Effects of Mass Imbalance in the Normal State of an Ultracold Fermi Gas in the BCS-BEC Crossover Region