Hydrodynamic tails and a fluctuation bound on the bulk viscosity

Journal Article · Tue Dec 05 00:00:00 EST 2017 · Physical Review A

DOI:https://doi.org/10.1103/physreva.96.063607· OSTI ID:1540672

Martinez, Mauricio ^[1]; Schäfer, Thomas ^[1]

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1. North Carolina State Univ., Raleigh, NC (United States)

Here, we study the small frequency behavior of the bulk viscosity spectral function using stochastic fluid dynamics. We obtain a number of model independent results, including the long-time tail of the bulk stress correlation function and the leading nonanalyticity of the spectral function at small frequency. We also establish a lower bound on the bulk viscosity which is weakly dependent on assumptions regarding the range of applicability of fluid dynamics. The bound on the bulk viscosity $$ζ$$ scales as $$ζ_{min} ~( P - \frac{2}{3}\mathscr{E}) ^2Σ_iD_i^{-2}$$, where $$D_i$$ are the diffusion constants for energy and momentum and $$P - \frac{2}{3}\mathscr{E}$$, where $$P$$ is the pressure and $$\mathscr{E}$$ is the energy density, is a measure of scale breaking. Applied to the cold Fermi gas near unitarity, $$|λ/a_s| ≳ 1$$, where $$λ$$ is the thermal de Broglie wavelength and $$a_s$$ is the s-wave scattering length, this bound implies that the ratio of bulk viscosity to entropy density satisfies $$ζ/s ≳ 0.1ℏ/k_B$$. Here, $$ℏ$$ is Planck's constant and $$k_B$$ is Boltzmann's constant.

• Research Organization: North Carolina State University, Raleigh, NC (United States)
• Sponsoring Organization: USDOE Office of Science (SC); National Science Foundation (NSF)
• Grant/Contract Number: FG02-03ER41260; PHY-1607611
• OSTI ID: 1540672
• Alternate ID(s): OSTI ID: 1411269
• Journal Information: Physical Review A, Vol. 96, Issue 6; ISSN 2469-9926
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
optics
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quantum fluids & solids
stochastic dynamical systems