Geodesic
Some features of quantum statistical systems with an energy spectrum of the fractional-power type
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 404-416 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We derive and investigate the equation of state for a system with a fractional-power spectrum and also derive an expression for the density of states in such systems. We consider a fractional-differential model of electron–phonon interaction.
Keywords: fractional-order derivative, equation of state, nonlocality. 
@article{TMF_2012_171_3_a3,
     author = {Z. Z. Alisultanov and R. P. Meylanov},
     title = {Some features of quantum statistical systems with an~energy spectrum of the~fractional-power type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {404--416},
     year = {2012},
     volume = {171},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a3/}
}
TY  - JOUR
AU  - Z. Z. Alisultanov
AU  - R. P. Meylanov
TI  - Some features of quantum statistical systems with an energy spectrum of the fractional-power type
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 404
EP  - 416
VL  - 171
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a3/
LA  - ru
ID  - TMF_2012_171_3_a3
ER  - 
%0 Journal Article
%A Z. Z. Alisultanov
%A R. P. Meylanov
%T Some features of quantum statistical systems with an energy spectrum of the fractional-power type
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 404-416
%V 171
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a3/
%G ru
%F TMF_2012_171_3_a3
Z. Z. Alisultanov; R. P. Meylanov. Some features of quantum statistical systems with an energy spectrum of the fractional-power type. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 404-416. http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a3/

[1] R. Hilfer (ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000 | MR | Zbl

[2] V. V. Uchaikin, Metod drobnykh proizvodnykh, Artishok, Ulyanovsk, 2008

[3] K. V. Chukbar, ZhETF, 108:5 (1995), 1875–1884

[4] R. P. Meilanov, M. S. Yanpolov, Pisma v ZhTF, 28:1 (2002), 67–73 | DOI | MR

[5] R. P. Meilanov, M. R. Shabanova, ZhTF, 81:7 (2011), 1–6 | DOI

[6] R. T. Sibatov, V. V. Uchaikin, UFN, 179:10 (2009), 1079–1104 | DOI

[7] V. V. Uchaikin, ZhETF, 124:4 (2003), 903–920 | DOI

[8] F. J. Dyson, Commun. Math. Phys., 12:2 (1969), 91–107 | DOI | MR

[9] F. J. Dyson, Commun. Math. Phys., 12:3 (1969), 212–215 | DOI | MR

[10] F. J. Dyson, Commun. Math. Phys., 21:4 (1971), 269–283 | DOI | MR

[11] N. Laskin, G. Zaslavsky, Physica A, 368:1 (2006), 38–54 | DOI

[12] V. S. Vladimirov, I. V. Volovich, E. I. Zelenov, p-Adicheskii analiz i matematicheskaya fizika, Nauka, M., 1994 | MR | Zbl

[13] N. Laskin, Phys. Lett. A, 268:4–6 (2000), 298–305 | DOI | MR | Zbl

[14] N. Laskin, Phys. Rev. E, 62:3 (2000), 3135–3145 | DOI | MR

[15] Z. Z. Alisultanov, R. P. Meilanov, Nelineinyi mir, 9:7 (2011), 461–467

[16] Z. Z. Alisultanov, R. P. Meilanov, Nelineinyi mir, 9:7 (2011), 470–476

[17] C. G. Samko, F. F. Kilbas, O. I. Marichev, Integraly i proizvodnye drobnogo poryadka i nekotorye prilozheniya, Nauka i tekhnika, Minsk, 1987 | MR | Zbl

[18] A. A. Potapov, Fraktaly v radiofizike i radiolokatsii: Topologiya vyborki, Universitetskaya kniga, M., 2005

[19] L. Kadanov, G. Beim, Kvantovaya statisticheskaya mekhanika, Mir, M., 1964 | MR | Zbl

[20] S. Sh. Rekhviashvili, Pisma v ZhTF, 30:22 (2004), 65–69 | DOI

[21] S. Sh. Rekhviashvili, ZhTF, 78:12 (2008), 54–58 | DOI

[22] V. M. Kuznetsov, V. I. Khromov, ZhTF, 78:11 (2008), 11–16 | DOI

[23] I. A. Kvasnikov, Termodinamika i statisticheskaya fizika, v. 4, Kvantovaya statistika, URSS, M., 2002 | MR

[24] A. N. Kozlov, V. N. Flerov, Pisma v ZhETF, 25:1 (1977), 54–58

[25] V. F. Grin, D. S. Lepsveridze, E. A. Salkov, G. A. Shepelskii, Pisma v ZhETF, 21:7 (1975), 415–418

[26] E. G. Maksimov, Sh. Van, M. V. Magnitskaya, S. V. Ebert, Pisma v ZhETF, 87:8 (2008), 507–510 | DOI

[27] V. M. Eleonskii, V. G. Korolev, N. E. Kulagin, Pisma v ZhETF, 76:12 (2002), 859–862 | DOI

[28] Yu. E. Lozovik, S. P. Merkulova, A. A. Sokolik, UFN, 178:7 (2008), 757–776 | DOI | DOI

[29] G. Savini, A. C. Ferrari, F. Giustino, Phys. Rev. Lett., 105 (2010), 037002, 4 pp. | DOI

[30] A. V. Milovanov, J. J. Rasmussen, Phys. Rev. B, 66:13 (2002), 134505, 11 pp., arXiv: cond-mat/0201504 | DOI

[31] X.-B. Wang, J.-X. Li, Q. Jiang, Z.-H. Zhang, Phys. Rev. B, 49:14 (1994), 9778–9781 | DOI

[32] V. V. Zosimov, L. M. Lyamshev, UFN, 165:4 (1995), 361–402 | DOI

[33] L. M. Zelenyi, A. V. Milovanov, UFN, 174:8 (2004), 809–852 | DOI