Two-fluid hydrodynamics of a Bose gas including damping from normal fluid transport coefficients

We extend our recent work on the two-fluid hydrodynamics of the condensate and noncondensate in a trapped Bose gas by including the dissipation associated with viscosity and thermal conduction in the thermal cloud. For purposes of illustration, we consider the hydrodynamic modes in the case of a uniform Bose gas. A finite thermal conductivity and shear viscosity give rise to a damping of the first and second sound modes, in addition to the damping found previously due to the lack of diffusive equilibrium between the condensate and noncondensate. The relaxational mode associated with this equilibration process is strongly coupled to thermal fluctuations and reduces to the usual thermal diffusion mode above the Bose-Einstein transition. In contrast to the standard Landau two-fluid hydrodynamics, we predict a damped mode centered at zero frequency, in addition to the usual second sound doublet.PACS Nos.: 03.75.Fi, 05.30Jp, 67.40.Db

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Hydrodynamic modes in 3He–4He mixtures at the critical point

Canadian Journal of Physics ◽

10.1139/p69-057 ◽

1969 ◽

Vol 47 (4) ◽

pp. 429-434 ◽

Cited By ~ 29

Author(s):

Allan Griffin

Keyword(s):

Critical Point ◽

Second Sound ◽

Diffusion Mode ◽

Hydrodynamic Modes ◽

Fluid Hydrodynamics ◽

Two Fluid ◽

Critical Mixing

At the critical mixing point of 3He–4He mixtures, the amplitudes of both the nonpropagating diffusion mode and second sound may become anomalously large. The damping of these two critical modes is discussed on the basis of Khalatnikov's two-fluid hydrodynamics.

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Critical behaviour of hydrodynamic series

Journal of High Energy Physics ◽

10.1007/jhep05(2021)287 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

M. Asadi ◽

H. Soltanpanahi ◽

F. Taghinavaz

Keyword(s):

Chemical Potential ◽

Transport Coefficients ◽

Hydrodynamic Modes ◽

Third Order ◽

Hydrodynamic Mode ◽

Strongly Coupled ◽

Conformal Theory ◽

Shear Dispersion ◽

Type Iib String Theory ◽

Hydrodynamic Transport

Abstract We investigate the time-dependent perturbations of strongly coupled $$ \mathcal{N} $$ N = 4 SYM theory at finite temperature and finite chemical potential with a second order phase transition. This theory is modelled by a top-down Einstein-Maxwell-dilaton description which is a consistent truncation of the dimensional reduction of type IIB string theory on AdS5×S5. We focus on spin-1 and spin-2 sectors of perturbations and compute the linearized hydrodynamic transport coefficients up to the third order in gradient expansion. We also determine the radius of convergence of the hydrodynamic mode in spin-1 sector and the lowest non-hydrodynamic modes in spin-2 sector. Analytically, we find that all the hydrodynamic quantities have the same critical exponent near the critical point θ = $$ \frac{1}{2} $$ 1 2 . Moreover, we propose a relation between symmetry enhancement of the underlying theory and vanishing of the only third order hydrodynamic transport coefficient θ1, which appears in the shear dispersion relation of a conformal theory on a flat background.

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Scattering of light from entropy fluctuations in 3He–4He mixtures

Canadian Journal of Physics ◽

10.1139/p68-529 ◽

1968 ◽

Vol 46 (17) ◽

pp. 1895-1903 ◽

Cited By ~ 15

Author(s):

B. N. Ganguly ◽

A. Griffin

Keyword(s):

Critical Point ◽

Concentration Fluctuations ◽

Complete Analysis ◽

Second Sound ◽

Hydrodynamic Equations ◽

Normal Fluid ◽

Strongly Coupled ◽

Scattering Of Light ◽

First Sound ◽

Scatter Light

In 1957, Gor'kov and Pitaevskii showed that second sound in 3He–4He mixtures is strongly coupled into the concentration fluctuations, which, in turn, scatter light quite strongly (especially near the critical point). In this paper, we give a more complete analysis of the fluctuations in density, entropy, and concentration. Our discussion is based on the hydrodynamic equations of Khalatnikov, which assume that the 3He atoms move with the normal fluid, and for simplicity we omit all dissipative coefficients. If we limit ourselves to scattering from density and concentration fluctuations, our results for the first and second sound intensities agree essentially with those of Gor'kov and Pitaevskii. Near the critical point, second sound scatters light about six times more strongly than first sound does.

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