Quantum Chaos for the Unitary Fermi Gas from the Generalized Boltzmann Equations

Abstract

In this paper, we study the chaotic behavior of the unitary Fermi gas in both high and low temperature limits by calculating the Quantum Lyapunov exponent defined in terms of the out-of-time-order correlator. We take the method of generalized Boltzmann equations derived from the augmented Keldysh approach \cite{augKeldysh}. At high temperature, the system is described by weakly interacting fermions with two spin components and the Lyapunov exponent is found to be ${\lambda }_L=21\frac{n}{T^{1/2}}$. Here $n$ is the density of fermions for a single spin component. In the low temperature limit, the system is a superfluid and can be described by phonon modes. Using the effective action derived in \cite{Son}, we find ${\lambda }_L=9\times 10^3{\left(\frac{T}{T_F}\right)}^{4}T$ where $T_F$ is the Fermi energy. By comparing these to existing results of heat conductivity, we find that $D_E\ll v^2/{\lambda }_L$ where $D_E$ is the energy diffusion constant and $v$ is some typical velocity. We argue that this is related to the conservation law for such systems with quasi-particles.

8 pages, 5 figures

References in corpus (18)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Theory of universal incoherent metallic transport
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Universal Quantum Viscosity in a Unitary Fermi Gas
• Holographic quantum matter
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Quantum chaos on a critical Fermi surface
• Onset of many-body chaos in the $O(N)$ model
• Quantum butterfly effect in weakly interacting diffusive metals
• The Shear Viscosity to Entropy Density Ratio of Trapped Fermions in the Unitarity Limit
• An upper bound on transport
• Density Functional Theory for non-relativistic Fermions in the Unitarity Limit
• Scrambling in the Dicke model
• Hierarchy of Information Scrambling, Thermalization, and Hydrodynamic Flow in Graphene
• Energy absorption spectroscopy of unitary Fermi gases in a uniform potential
• Viscosity spectral function of a scale invariant non-relativistic fluid from holography

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