Viscosity spectral functions of resonating fermions in the quantum virial expansion

Nishida, Yusuke

doi:10.1016/j.aop.2019.167949

Cited by 40 publications

(41 citation statements)

References 42 publications

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“…Note added: While this manuscript was being completed, Refs. [71,72] appeared, which discuss the virial expansion of the viscosity spectral functions using other methods and have some overlap with this work. Overlapping results are in agreement.…”

Section: Discussionmentioning

confidence: 99%

High-temperature expansion of the viscosity in interacting quantum gases

Hofmann

2020

Phys. Rev. A

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We compute the frequency-dependent shear and bulk viscosity spectral functions of an interacting Fermi gas in a quantum virial expansion up to second quadratic order in the fugacity parameter z = e βµ , which is small at high temperatures. Calculations are carried out using a diagrammatic finite-temperature field-theory framework, in which the analytic continuation from Matsubara to real frequencies is carried out in closed analytic form. Besides the zero-frequency Drude peak, our results for the spectral functions show a broad continuous spectrum at all frequencies with an additional bound state contribution for frequencies larger than the dimer-breaking energy. Our results are consistent with various sum rules and universal high-frequency tails. In the low-frequency limit, the shear viscosity spectral function is recast as a collision integral, which reproduces known results for the static shear viscosity from kinetic theory. Our findings for the static bulk viscosity of a Fermi gas near unitarity, however, show a non-analytic dependence on the scattering length, at variance with kinetic theory.

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Section: Discussionmentioning

confidence: 99%

High-temperature expansion of the viscosity in interacting quantum gases

Hofmann

2020

Phys. Rev. A

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“…In order to calculate the thermodynamic properties of the one dimensional anomalous Fermi gas, we perform the virial expansion to third order in the fugacity, z, following the arguments presented in Ref. [24]. We explicitly calculate the virial coefficients, Tan's contact, and bulk viscosity for the one dimensional anomalous fermions, and show that they are indeed proportional to arXiv:1910.06516v1 [cond-mat.quant-gas] 15 Oct 2019 their two dimensional counterparts.…”

Section: Introductionmentioning

confidence: 99%

Virial expansion for a three-component Fermi gas in one dimension: The quantum anomaly correspondence

Maki

Ordóñez

2019

Phys. Rev. A

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In this paper we explore the transport properties of three-component Fermi gases confined to one spatial dimension, interacting via a three-body interaction, in the high temperature limit. At the classical level, the three-body interaction is scale invariant in one dimension. However, upon quantization, an anomaly appears which breaks the scale invariance. This is very similar to the physics of two-component fermions in two spatial dimensions, where the two-body interaction is also anomalous. Previous studies have already hinted that the physics of these two systems are intimately related. Here we expand upon those studies by examining the thermodynamic properties of this anomalous one dimensional system in the high temperature limit. We show there is an exact mapping between the traditional two-body anomalous interaction in two dimensions, to that of three-body interaction in one dimension. This result is valid in the high temperature limit, where the thermodynamics can be understood in terms of few-body correlations.

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“…We focus on mesoscopic systems with a small particle number, which are in the quasi-2D regime, and describe the gas to leading linear order in the interaction strength g by means of (degenerate) perturbation theory. At this order, scale invariance is exact, with logarithmic corrections only entering at higher order: Indeed, experimental signatures of scale invariance breaking -such as a shift in the breathing mode frequency [19], logarithmic corrections to the rf-spectrum [40], or a finite bulk viscosity [41][42][43] -only start at second order in the interaction parameter g(κ). Moreover, on a formal level, the quantum anomaly is manifest in the commutator between D and H, which reads [D, H] = 2iH − 2iI [19].…”

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confidence: 99%

Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases

Bekassy,

Hofmann

2021

Preprint

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Two-dimensional Fermi gases with universal short-range interactions are known to exhibit a quantum anomaly, where a classical scale and conformal invariance is broken by quantum effects at strong coupling. We argue that in a quasi two-dimensional geometry, a conformal window remains at weak interactions. Using degenerate perturbation theory, we verify the conformal symmetry by computing the energy spectrum of mesoscopic particle ensembles in a harmonic trap, which separates into conformal towers formed by so-called primary states and their center-of-mass and breathing-mode excitations, the latter having excitation energies at precisely twice the harmonic oscillator energy. In addition, using Metropolis importance sampling, we compute the hyperradial distribution function of the many-body wavefunctions, which are predicted by the conformal symmetry in closed analytical form. The weakly interacting Fermi gas constitutes a system where the non-relativistic conformal symmetry can be revealed using elementary methods, and our results are testable in current experiments on mesoscopic Fermi gases.

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Viscosity spectral functions of resonating fermions in the quantum virial expansion

Cited by 40 publications

References 42 publications

High-temperature expansion of the viscosity in interacting quantum gases

High-temperature expansion of the viscosity in interacting quantum gases

Virial expansion for a three-component Fermi gas in one dimension: The quantum anomaly correspondence

Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases

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