Geodesic
Calculation of correlation functions in totally asymmetric exactly solvable models on a ring
Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 3, pp. 370-378 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider exactly solvable totally asymmetric models of low-dimensional nonequilibrium statistical physics on a periodic chain, namely, the totally asymmetric simple exclusion process and the totally asymmetric simple zero-range process. We describe the method for calculating correlation functions for the models on a periodic lattice and represent scalar products of state vectors of the model as determinants.
Keywords: asymmetric process, integrable system, correlation function. 
@article{TMF_2013_175_3_a4,
     author = {N. M. Bogolyubov},
     title = {Calculation of correlation functions in totally asymmetric exactly solvable models on a~ring},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {370--378},
     year = {2013},
     volume = {175},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a4/}
}
TY  - JOUR
AU  - N. M. Bogolyubov
TI  - Calculation of correlation functions in totally asymmetric exactly solvable models on a ring
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2013
SP  - 370
EP  - 378
VL  - 175
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a4/
LA  - ru
ID  - TMF_2013_175_3_a4
ER  - 
%0 Journal Article
%A N. M. Bogolyubov
%T Calculation of correlation functions in totally asymmetric exactly solvable models on a ring
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2013
%P 370-378
%V 175
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a4/
%G ru
%F TMF_2013_175_3_a4
N. M. Bogolyubov. Calculation of correlation functions in totally asymmetric exactly solvable models on a ring. Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 3, pp. 370-378. http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a4/

[1] C. T. MacDonald, J. H. Gibbs, A. C. Pipkin, Biopolimers, 6:1 (1968), 1–25 | DOI | MR

[2] L.-H. Gwa, H. Spohn, Phys. Rev. A, 46:2 (1992), 844–854 | DOI

[3] B. Derrida, J. Lebowitz, Phys. Rev. Lett., 80:2 (1998), 209–213, arXiv: cond-mat/9809044 | DOI | MR | Zbl

[4] M. R. Evans, Brazilian J. Phys., 30:1 (2000), 42–57 | DOI

[5] V. B. Priezzhev, Phys. Rev. Lett., 91:5 (2003), 050601, 4 pp., arXiv: cond-mat/0211052 | DOI

[6] A. M. Povolotsky, Phys. Rev. E, 69:6 (2004), 061109, 7 pp., arXiv: cond-mat/0401249 | DOI | MR

[7] M. Prähofer, H. Spohn, J. Statist. Phys., 115:1–2 (2004), 255–279, arXiv: cond-mat/0212519 | DOI | MR | Zbl

[8] O. Golinelli, K. Mallick, J. Phys. A, 37:10 (2004), 3321–3331, arXiv: cond-mat/0312371 | DOI | MR | Zbl

[9] M. R. Evans, T. Hanney, J. Phys. A, 38:19 (2005), R195–R240, arXiv: cond-mat/0501338 | DOI | MR | Zbl

[10] V. B. Priezzhev, Pramana, 64:6 (2005), 915–925 | DOI

[11] A. M. Povolotsky, J. F. F. Mendes, J. Statist. Phys., 123:1 (2006), 125–166, arXiv: cond-mat/0411558 | DOI | MR | Zbl

[12] A. M. Povolotsky, V. B. Priezzhev, J. Stat. Mech., 2006, P07002, 28 pp., arXiv: cond-mat/0605150 | DOI

[13] M. Kanai, J. Phys. A, 40:26 (2007), 7127–7138, arXiv: cond-mat/0701190 | DOI | MR | Zbl

[14] A. Borodin, P. Ferrari, M. Prahofer, T. Sasamoto, J. Statist. Phys., 129:5–6 (2007), 1055–1080, arXiv: math-ph/0608056 | DOI | MR | Zbl

[15] A. M. Povolotsky, V. B. Priezzhev, J. Stat. Mech., 8 (2007), P08018, 27 pp. | DOI | MR

[16] S. Prolhac, K. Mallick, J. Phys. A, 41:17 (2008), 175002, 20 pp., arXiv: 0801.4659 | DOI | MR | Zbl

[17] N. M. Bogoliubov, SIGMA, 5 (2009), 052, 11 pp., arXiv: 0904.3680 | DOI | MR | Zbl

[18] Y. Yamada, M. Katori, Phys. Rev. E, 84:4 (2011), 041141, 8 pp., arXiv: 1108.0753 | DOI

[19] L. D. Faddeev, Sov. Sci. Rev. Math. C, 1 (1980), 107–155 ; “Quantum completely integrable models in field theory”, 40 Years in Mathematical Physics, World Scientific Series in 20th Century Mathematics, 2, World Sci., Singapore, 1995, 187–235 | Zbl | DOI | MR

[20] P. P. Kulish, E. K. Sklyanin, “Quantum spectral transform method recent developments”, Integrable Quantum Field Theories (Tvärminne, Finland, 23–27 March, 1981), Lecture Notes in Physics, 151, eds. J. Hietarinta, C. Montonen, Springer, Berlin, 1982, 61–119 | DOI | MR

[21] V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Univ. Press, Cambridge, 1993 | DOI | MR | Zbl

[22] N. M. Bogolyubov, A. G. Izergin, V. E. Korepin, Korrelyatsionnye funktsii integriruemykh sistem i kvantovyi metod obratnoi zadachi, Nauka, M., 1992 | MR

[23] J. D. Noh, D. Kim, Phys. Rev. E, 49:3 (1994), 1943–1961, arXiv: cond-mat/9312001 | DOI

[24] D. Kim, Phys. Rev. E, 52:4 (1995), 3512–3524 | DOI

[25] D. S. Lee, D. Kim, Phys. Rev. E, 59:6 (1999), 6476–6482, arXiv: cond-mat/9902001 | DOI

[26] N. M. Bogoliubov, T. Nassar, Phys. Lett. A, 234:5 (1997), 345–350 | DOI | MR | Zbl

[27] O. Golinelli, K. Mallick, J. Phys. A, 39:41 (2006), 12679–12705, arXiv: cond-mat/0611701 | DOI | MR | Zbl

[28] N. M. Bogoliubov, A. G. Izergin, N. A. Kitanine, Nucl. Phys. B, 516:3 (1998), 501–528 | DOI | MR | Zbl

[29] N. M. Bogolyubov, Zap. nauchn. semin. POMI, 398 (2012), 5–25 | MR

[30] N. M. Bogoliubov, J. Phys. A, 38:43 (2005), 9415–9430, arXiv: cond-mat/0503748 | DOI | MR | Zbl