Abstract
In this paper we investigate the scattering mechanisms of viscous momentum transport in unitary Fermi gases below the pseudogap temperature T* by opening almost all the elastic and inelastic scattering channels. For a given system Hamiltonian, we adopt a microscopic t-matrix approximation to determine the thermodynamical quantities, and we approach an equivalent three-fluid dynamics to calculate the viscous relaxation time τ by two kinds of elementary excitations. The exotic scattering processes raised by uncondensed Fermi pairs greatly decay τ and lead to a universal behavior of τ with temperature, which is closely related to the anomalous transport in a wide range of strongly correlated systems. For linking our findings of τ to the shear viscosity η, we present a Kubo-based expression of η by the stress-tensor correlation function with conserved vertex corrections, and we give an approximate relation for a possible experimental determination of τ. Our results fit well with measurements and are comparable with other theories. Moreover, we verify the newly proposed universal upper bound of the ratio of η and entropy density s in unitary Fermi gases.
Highlights
Many strongly correlated systems display a remarkable degree of universal anomalous behaviors in their transport properties, such as the quantum-limited values of diffusivity for diverse fluids from quark-gluon plasma [1,2] to ultracold Fermi gases [3,4,5], and the linear-in-temperature (T ) resistivity in a wide range of materials [6]
Some studies have found that τ exhibits the same temperature dependence as the characteristic Planck time τP = h/(kBT ) in the anomalous transport regions [6,8,9] (h = kB = 1 hereafter), and some conjectures proposed that τ could lead to the universal behaviors of transport coefficients by controlling the universal lower and upper bounds [10,11]
We can give the second kind of elementary excitation: since this is a single-component Fermi system, we can alternatively treat the elementary excitations of the system approximately as only fermions, while the composite bosons play a medium role in the three-fluid dynamics [36]
Summary
Many strongly correlated systems display a remarkable degree of universal anomalous behaviors in their transport properties, such as the quantum-limited values of diffusivity for diverse fluids from quark-gluon plasma [1,2] to ultracold Fermi gases [3,4,5], and the linear-in-temperature (T ) resistivity in a wide range of materials [6]. The shear viscosity is closely related to the transverse momentum diffusion coefficient Dη = η/(sT ) in a wide class of interacting systems This bound has been generalized to any diffusion D v2/T with the typical velocity scale v [8,9].
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