RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

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

DOI: https://doi.org/10.4213/tmf115

Full text: PDF file (205 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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
\Bibitem{Nem04} \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 \mathnet{http://mi.mathnet.ru/tmf115} \crossref{https://doi.org/10.4213/tmf115} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2036109} \zmath{https://zbmath.org/?q=an:1178.82013} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2004TMP...141.1452N} \transl \jour Theoret. and Math. Phys. \yr 2004 \vol 141 \issue 1 \pages 1452--1460 \crossref{https://doi.org/10.1023/B:TAMP.0000043860.52270.0c} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000225149500009} 

• http://mi.mathnet.ru/eng/tmf115
• https://doi.org/10.4213/tmf115
• http://mi.mathnet.ru/eng/tmf/v141/i1/p141

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
3. Mongiovi, MS, “Energy and temperature of superfluid turbulent vortex tangles”, Physical Review B, 75:21 (2007), 214514
4. Alamri, SZ, “Reconnection of Superfluid Vortex Bundles”, Physical Review Letters, 101:21 (2008), 215302
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
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
7. Nemirovskii, SK, “Langevin Dynamics of Vortex Lines and Thermodynamic Equilibrium of Vortex Tangle”, Journal of Low Temperature Physics, 156:3–6 (2009), 182
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
9. Nemirovskii S.K., “Quantum Turbulence: Theoretical and Numerical Problems”, Phys. Rep.-Rev. Sec. Phys. Lett., 524:3 (2013), 85–202
10. Kivotides D., “Energy Spectra of Finite Temperature Superfluid Helium-4 Turbulence”, Phys. Fluids, 26:10 (2014), 105105
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
12. Bustamante M.D., Nazarenko S., “Derivation of the Biot-Savart Equation From the Nonlinear Schrodinger Equation”, Phys. Rev. E, 92:5 (2015), 053019
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
14. Nemirovskii S.K., “Thermal Equilibrium of Vortex Lines in Counterflowing He II”, J. Low Temp. Phys., 185:5-6 (2016), 365–370
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
16. Quantum Electron., 48:5 (2018), 405–409
17. Nemirovskii S.K., “Stochastic Motion of Vortex Filaments in He II Under Random Force”, Low Temp. Phys., 44:10 (2018), 994–1000
18. Nemirovskii S.K., “Chaotic Quantum Vortices in He II: Thermodynamic Equilibrium and Turbulence”, J. Eng. Thermophys., 27:4 (2018), 415–421
•  Number of views: This page: 233 Full text: 78 References: 35 First page: 2