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TMF, 2004, Volume 141, Number 1, Pages 141–151 (Mi tmf115)  

This article is cited in 18 scientific papers (total in 18 papers)

Thermodynamic Equilibrium in the System of Chaotic Quantized Vortices in a Weakly Imperfect Bose Gas

S. K. Nemirovskii

Institute of Thermophysics, Siberian Branch of the Russian Academy of Science

Abstract: In the example of a weakly imperfect Bose gas, we discuss the mechanism of establishing thermodynamic equilibrium for a chaotic set of quantum vortex filaments. We assume that the dynamics of the Bose condensate is described by the Gross–Pitaevsky equation with an additional noise satisfying the fluctuation-dissipation theorem. In considering a vortex filament as the intersection line of surfaces on which the real and imaginary parts of the order parameter $\psi(\mathbf x,t)$ vanish, we obtain an equation of the Langevin type for elements of the vortex filament with an appropriately transformed random force. The Fokker–Planck equation for the probability density has a solution given by the Gibbs distribution at the temperature of the Bose condensate. In other words, when the Bose condensate is in thermal equilibrium and no other random actions exist, the system of vortices is also in thermal equilibrium.

Keywords: quantum vortex filaments, Bose gas, thermodynamic equilibrium, superfluid turbulence


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English version:
Theoretical and Mathematical Physics, 2004, 141:1, 1452–1460

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Received: 11.08.2003

Citation: S. K. Nemirovskii, “Thermodynamic Equilibrium in the System of Chaotic Quantized Vortices in a Weakly Imperfect Bose Gas”, TMF, 141:1 (2004), 141–151; Theoret. and Math. Phys., 141:1 (2004), 1452–1460

Citation in format AMSBIB
\by S.~K.~Nemirovskii
\paper Thermodynamic Equilibrium in the System of Chaotic Quantized Vortices in a~Weakly Imperfect Bose Gas
\jour TMF
\yr 2004
\vol 141
\issue 1
\pages 141--151
\jour Theoret. and Math. Phys.
\yr 2004
\vol 141
\issue 1
\pages 1452--1460

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    This publication is cited in the following articles:
    1. Nemirovskii SK, “Evolution of a network of vortex loops in He-II: Exact solution of the rate equation”, Physical Review Letters, 96:1 (2006), 015301  crossref  adsnasa  isi  scopus  scopus
    2. Kondaurova L., Nemirovskii S.K., “Numerical study of stochastic vortex tangle dynamics in superfluid He”, Low Temperature Physics, AIP Conference Proceedings, 850, no. A-B, 2006, 223–224  crossref  adsnasa  isi  scopus  scopus
    3. Mongiovi, MS, “Energy and temperature of superfluid turbulent vortex tangles”, Physical Review B, 75:21 (2007), 214514  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    4. Alamri, SZ, “Reconnection of Superfluid Vortex Bundles”, Physical Review Letters, 101:21 (2008), 215302  crossref  adsnasa  isi  elib  scopus  scopus
    5. Nemirovskii, SK, “Kinetics of a network of vortex loops in HeII and a theory of superfluid turbulence”, Physical Review B, 77:21 (2008), 214509  crossref  adsnasa  isi  elib  scopus  scopus
    6. Kondaurova, LP, “Numerical simulation of stochastic motion of vortex loops under action of random force. Evidence of the thermodynamic equilibrium state”, Journal of Engineering Thermophysics, 18:1 (2009), 65  crossref  isi  scopus  scopus
    7. Nemirovskii, SK, “Langevin Dynamics of Vortex Lines and Thermodynamic Equilibrium of Vortex Tangle”, Journal of Low Temperature Physics, 156:3–6 (2009), 182  crossref  adsnasa  isi  scopus  scopus
    8. Nemirovskii S.K., “Energy Spectrum of the 3D Velocity Field, Induced by Vortex Tangle”, J. Low Temp. Phys., 171:5-6 (2013), 504–510  crossref  adsnasa  isi  elib  scopus  scopus
    9. Nemirovskii S.K., “Quantum Turbulence: Theoretical and Numerical Problems”, Phys. Rep.-Rev. Sec. Phys. Lett., 524:3 (2013), 85–202  crossref  mathscinet  isi  scopus  scopus
    10. Kivotides D., “Energy Spectra of Finite Temperature Superfluid Helium-4 Turbulence”, Phys. Fluids, 26:10 (2014), 105105  crossref  adsnasa  isi  scopus  scopus
    11. Jou D., Mongiovi M.S., Sciacca M., “Spectral Energy Distribution and Generalized Wien's Law For Photons and Cosmic String Loops”, Phys. Scr., 89:7 (2014), 075002  crossref  mathscinet  adsnasa  isi  scopus  scopus
    12. Bustamante M.D., Nazarenko S., “Derivation of the Biot-Savart Equation From the Nonlinear Schrodinger Equation”, Phys. Rev. E, 92:5 (2015), 053019  crossref  mathscinet  adsnasa  isi  scopus  scopus
    13. Yukalov V.I., Novikov A.N., Bagnato V.S., “Realization of Inverse Kibble-Zurek Scenario With Trapped Bose Gases”, Phys. Lett. A, 379:20-21 (2015), 1366–1371  crossref  adsnasa  isi  elib  scopus  scopus
    14. Nemirovskii S.K., “Thermal Equilibrium of Vortex Lines in Counterflowing He II”, J. Low Temp. Phys., 185:5-6 (2016), 365–370  crossref  isi  scopus
    15. Van Gorder R.A., “Breathers and Nonlinear Waves on Open Vortex Filaments in the Nonrelativistic Abelian Higgs Model”, Phys. Rev. D, 95:9 (2017), 096007  crossref  isi  scopus  scopus
    16. Quantum Electron., 48:5 (2018), 405–409  mathnet  crossref  isi  elib
    17. Nemirovskii S.K., “Stochastic Motion of Vortex Filaments in He II Under Random Force”, Low Temp. Phys., 44:10 (2018), 994–1000  crossref  isi  scopus
    18. Nemirovskii S.K., “Chaotic Quantum Vortices in He II: Thermodynamic Equilibrium and Turbulence”, J. Eng. Thermophys., 27:4 (2018), 415–421  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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