×

Effective temperature and scaling laws of polarized quantum vortex bundles. (English) Zbl 1252.82076

Summary: An effective non-equilibrium temperature is defined for (locally) polarized and dense turbulent superfluid vortex bundles, related to the average energy of the excitations (Kelvin waves) of vortex lines. In the quadratic approximation of the excitation energy in terms of the wave amplitude \(A\), a previously known scaling relation between amplitude and wavelength \(k\) of Kelvin waves in polarized bundles, namely \(A\propto k - 1/2\), follows from the homogeneity of the effective temperature. This result is analogous to that of the well-known equipartition result in equilibrium systems.

MSC:

82C35 Irreversible thermodynamics, including Onsager-Machlup theory
82D50 Statistical mechanics of superfluids
76B47 Vortex flows for incompressible inviscid fluids
76F05 Isotropic turbulence; homogeneous turbulence
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Donnelly, R. J., Quantized Vortices in Helium II (1991), Cambridge University Press: Cambridge University Press Cambridge, UK
[2] Kozik, E.; Svistunov, B., J. Low Temp. Phys., 156, 215 (2009)
[3] Brown, T. M., J. Phys. A: Math. Gen., 15, 2285 (1982)
[4] Jou, D.; Mongiovì, M. S., Phys. Lett. A, 359, 183 (2006)
[5] Mongiovì, M. S.; Jou, D.; Sciacca, M., Phys. Rev. B, 75, 214514 (2007)
[6] Jou, D.; Mongiovì, M. S., Phys. Lett. A, 373, 2306 (2009)
[7] Barenghi, C. F.; Donnelly, R. J.; Vinen, W. F., Quantized Vortex Dynamics and Superfluid Turbulence (2001), Springer: Springer Berlin · Zbl 0972.00023
[8] Nemirovskii, S. K.; Fiszdon, W., Rev. Mod. Phys., 67, 37 (1995)
[9] Nemirovskii, S. K.; Lebedev, V. V., Sov. Phys. JETP, 57, 1009 (1983)
[10] Nemirovskii, S. K.; Nedoboiko, M. W., (Barenghi, C. F.; Donnelly, R. J.; Vinen, W. F., Quantized Vortex Dynamics and Superfluid Turbulence (2001), Springer: Springer Berlin), 205-211
[11] Jou, D.; Mongiovì, M. S.; Sciacca, M.; Barenghi, C. F., J. Phys. A: Math. Theor., 43, 205501 (2010)
[12] Jou, D.; Casas-Vázquez, J.; Lebon, G., Extended Irreversible Thermodynamics (2010), Springer: Springer Berlin · Zbl 1185.74002
[13] Casas-Vázquez, J.; Jou, D., Rep. Prog. Phys., 66, 1937 (2003)
[14] Crisanti, A.; Ritort, F., J. Phys. A: Math. Gen., 36, R181 (2003)
[15] Makse, H. A.; Kurchan, J., Nature, 415, 614 (2002)
[16] Baranyai, A., Phys. Rev. E, 61, R3306 (2000)
[17] Morriss, G. P.; Rondoni, L., Phys. Rev. E, 59, R5 (1999)
[18] Criado-Sancho, A.; Jou, D.; Casas-Vázquez, J., Phys. Lett. A, 350, 339 (2006)
[19] Jou, D.; Mongiovì, M. S.; Sciacca, M., Phys. Rev. D, 83, 043519 (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.