Quasi-averages in the solution of the classification problem for equilibriums of condensed media with
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 2, pp. 290-303 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We develop a statistical approach for solving the classification problem for equilibriums of degenerate condensed media. We introduce generators of unbroken and spatial symmetries of an equilibrium and use them to derive the classification equations for the order parameter. We elucidate the mechanism of the appearance of additional thermodynamic parameters characterizing both homogeneous and inhomogeneous equilibriums. We solve the classification problem for equilibriums of various liquid crystals analytically.
Keywords: equilibrium, quasi-average, order parameter, liquid crystal, thermodynamic parameter.
Mots-clés : classification equation
@article{TMF_2009_160_2_a4,
     author = {M. Yu. Kovalevsky},
     title = {Quasi-averages in the~solution of the~classification problem for equilibriums of condensed media with},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {290--303},
     year = {2009},
     volume = {160},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a4/}
}
TY  - JOUR
AU  - M. Yu. Kovalevsky
TI  - Quasi-averages in the solution of the classification problem for equilibriums of condensed media with
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 290
EP  - 303
VL  - 160
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a4/
LA  - ru
ID  - TMF_2009_160_2_a4
ER  - 
%0 Journal Article
%A M. Yu. Kovalevsky
%T Quasi-averages in the solution of the classification problem for equilibriums of condensed media with
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 290-303
%V 160
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a4/
%G ru
%F TMF_2009_160_2_a4
M. Yu. Kovalevsky. Quasi-averages in the solution of the classification problem for equilibriums of condensed media with. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 2, pp. 290-303. http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a4/

[1] N. Bogolubov, Physica, 26, Suppl. 1 (1960), s1–s16 | DOI

[2] N. N. Bogolyubov, N. N. Bogolyubov (ml.), Vvedenie v kvantovuyu statisticheskuyu mekhaniku, Nauka, M., 1984 | MR | MR | Zbl

[3] A. I. Akhiezer, S. V. Peletminskii, Metody statisticheskoi fiziki, Nauka, M., 1977 | MR | MR

[4] N. N. Bogolyubov (ml.), M. Yu. Kovalevskii, A. M. Kurbatov, S. V. Peletminskii, A. N. Tarasov, UFN, 159:4 (1989), 585–620 | DOI | MR

[5] M. Yu. Kovalevskii, S. V. Peletminskii, EChAYa, 33:6 (2002), 1357–1445

[6] M. Yu. Kovalevskii, S. V. Peletminskii, Statisticheskaya mekhanika kvantovykh zhidkostei i kristallov, Fizmatlit, M., 2006

[7] L. D. Landau, ZhETF, 7 (1937), 18–33 ; “К теории фазовых переходов. I”, Собрание трудов, Т. 1, ред. Б. М. Лифшиц, Наука, М, 1969, 234–252 | Zbl | MR

[8] G. Barton, M. A. Moore, J. Phys. C, 7:17 (1974), 2989–3000 | DOI

[9] P. G. de Gennes, J. Prost, The Physics of Liquid Crystals, Oxford Univ. Press, Oxford, 1995

[10] M. Kleman, O. D. Lavrentovich, Osnovy fiziki chastichno uporyadochennykh sred, Fizmatlit, M., 2007

[11] D. Belitz, T. R. Kirkpatrick, T. Vojta, Rev. Modern Phys., 77:2 (2005), 579–632 | DOI

[12] V. P. Mineev, Sov. Sci. Rev. A, 2 (1980), 173–246; Topologically Stable Defects and Solitons in Ordered Media, Classic Rev. Phys., 1, Harwood Academic, Amsterdam, 1998 | MR | Zbl

[13] F. W. Nijhoff, H. W. Capel, A. Breems, Phys. A, 130:3 (1985), 375–411 | DOI | MR

[14] A. M. J. Schakel, F. A. Bais, J. Phys., 1:9 (1989), 1743–1752 | DOI

[15] H. W. Capel, “Group theory and phases of superfluid $^3\mathrm{He}$”, Selected Topics in Statistical Mechanics, eds. A. A. Logunov, N. N. Bogolubov, Jr., V. G. Kadyshevsky A. S. Shumovsky, World Sci., Teaneck, NJ, 1990, 73–83 | MR | Zbl

[16] D. Vollhardt, P. Wölfle, The Superfluid Phases of Helium 3, Taylor Francis, New York, 1990

[17] E. Kats, V. V. Lebedev, Dinamika zhidkikh kristallov, URSS, M., 1988

[18] A. V. Finkelshtein, O. B. Ptitsin, Fizika belka, Kurs lektsii, Knizhnyi Dom “Universitet”, M., 2002

[19] N. N. Bogolyubov (ml.), M. Yu. Kovalevskii, UFZh, 50:8A (2005), A104–A112 | MR

[20] D. A. Demyanenko, M. Yu. Kovalevskii, FNT, 33:11 (2007), 1271–1281

[21] A. P. Ivashin, M. Yu. Kovalevskii, N. N. Chekanova, FNT, 30:9 (2004), 920–927

[22] M. Y. Kovalevskii, A. A. Rozhkov, L. V. Logvinova, Phys. A, 336:3–4 (2004), 271–293 | DOI