Geodesic
Classification of the Equilibrium States of $^{3}$He
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 1, pp. 159-176 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Based on the concept of quasiaverages, we classify the equilibrium states of the superfluid $^{3}$He with due regard to possible inhomogeneous structures. We establish a relation of the residual and spatial symmetry conditions to a helicoidal ordering of the spatial anisotropy vector and a spiral structure of the magnetic anisotropy vector. We show that the set of anisotropic homogeneous equilibrium states can be classified in terms of two quantum numbers corresponding to the projections of the Cooper-pair spin and orbital momentum onto the anisotropy directions.
Keywords: superfluidity, $^{3}$He, equilibrium, order parameter, quasiaverages, triplet pairing.
Mots-clés : classification 
@article{TMF_2003_135_1_a8,
     author = {M. Yu. Kovalevsky and S. V. Peletminskii and N. N. Chekanova},
     title = {Classification of the {Equilibrium} {States} of $^{3}${He}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {159--176},
     year = {2003},
     volume = {135},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a8/}
}
TY  - JOUR
AU  - M. Yu. Kovalevsky
AU  - S. V. Peletminskii
AU  - N. N. Chekanova
TI  - Classification of the Equilibrium States of $^{3}$He
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 159
EP  - 176
VL  - 135
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a8/
LA  - ru
ID  - TMF_2003_135_1_a8
ER  - 
%0 Journal Article
%A M. Yu. Kovalevsky
%A S. V. Peletminskii
%A N. N. Chekanova
%T Classification of the Equilibrium States of $^{3}$He
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 159-176
%V 135
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a8/
%G ru
%F TMF_2003_135_1_a8
M. Yu. Kovalevsky; S. V. Peletminskii; N. N. Chekanova. Classification of the Equilibrium States of $^{3}$He. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 1, pp. 159-176. http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a8/

[1] D. D. Osheroff, R. C. Richardson, D. M. Lee, Phys. Rev. Lett., 28 (1972), 885 ; A. J. A. Leggett, Rev. Mod. Phys., 47:2 (1975), 331 ; P. W. Anderson, W. F. Brinkman, “Theory of anisotropic superfluidity in $^3$He”, The Physics of Liquid and Solid Helium, Part II, eds. K. H. Bennemann, J. B. Ketterson, Wiley, New York, 1978, 177; В. П. Минеев, УФН, 139 (1983), 303 ; П. Н. Брусов, В. Н. Попов, Сверхтекучесть и коллективные свойства квантовых жидкостей, Наука, М., 1988; D. Vollhardt, P. Wolfle, The Superfluid Phases of Helium 3, Taylor, London, 1990; G. E. Volovick, Exotic Properties of Superfluid $^{3}\mathrm{He}$, World Scientific, Singapore, 1992 | DOI | DOI | DOI

[2] L. P. Pitaevskii, ZhETF, 37 (1959), 1794 | Zbl

[3] R. Balian, N. R. Werthamer, Phys. Rev., 131 (1963), 1553 | DOI | MR

[4] P. W. Anderson, P. Morel, Phys. Rev., 123 (1961), 1911 | DOI | MR

[5] V. Ambegaokar, N. D. Mermin, Phys. Rev. Lett., 30 (1973), 81 | DOI

[6] Z. M. Galasiewicz, Acta Phys. Polon., 19 (1960), 467 | Zbl

[7] G. Barton, M. Moore, J. Phys. C, 7 (1974), 4220 | DOI

[8] C. M. Varma, N. R. Werthamer, Phys. Rev. A, 9 (1974), 1465 | DOI | MR

[9] G. E. Volovik, Pisma v ZhETF, 63 (1996), 281; G. Baramidze, G. Kharadze, ЖЭТФ, 115:2 (1999), 754

[10] A. Korf, H. R. Brand, J. Low Temp. Phys., 109:1/2 (1997), 183

[11] F. W. Nijhoff, H. W. Capel, A. den Breems, Physica A, 130 (1985), 375 | DOI | MR

[12] F. W. Nijhoff, H. W. Capel, A. den Breems, Physica A, 135 (1986), 295 ; 139, 256 | DOI

[13] C. Bruder, D. Vollhardt, Phys. Rev. B, 34 (1986), 131 | DOI

[14] A. M. J. Schakel, F. A. Bais, J. Phys.: Cond. Matter, 1 (1989), 1743 | DOI

[15] A. Fetter, Phys. Rev. B, 20:1 (1979), 303 ; 23:5 (1981), 218; Y. R. Lin-Liu, D. Vollhardt, K. Maki, Phys. Rev. B, 20:1 (1979), 159 | DOI | DOI

[16] J. N. Kotzev, D. V. Shopova, Phys. Lett. A, 187 (1994), 264 | DOI

[17] V. M. Ruutu, J. Kopu, M. Krusius, U. Parts, B. Placais, E. V. Thuneberg, W. Xu, Phys. Rev. Lett., 79 (1997), 5058 ; J. Kopu, R. Hanninen, E. V. Thuneberg, Phys. Rev. B, 62 (2000), 12374 | DOI | DOI

[18] N. N. Bogoliubov, Physica, 26 (1960), 51

[19] N. N. Bogolyubov (ml.), M. Yu. Kovalevskii, A. M. Kurbatov, S. V. Peletminskii, A. N. Tarasov, UFN, 159:4 (1989), 585 | DOI

[20] M. Yu. Kovalevskii, S. V. Peletminskii, TMF, 100:1 (1994), 59

[21] M. Yu. Kovalevskii, A. A. Rozhkov, TMF, 127:2 (2001), 317 | DOI | Zbl

[22] N. N. Bogolyubov (ml.), M. Yu. Kovalevskii, A. M. Kurbatov, S. V. Peletminskii, A. N. Tarasov, EChAYa, 16 (1985), 875 | MR

[23] V. P. Mineev, Sov. Sci. Rev. A, 2 (1980), 173

[24] M. Yu. Kovalevskii, A. A. Rozhkov, TMF, 113:2 (1997), 313 | DOI

[25] A. I. Akhiezer, A. A. Isayev, S. V. Peletminsky, A. A. Yatsenko, Phys. Lett. B, 451 (1999), 430 | DOI