Geodesic
Exact solution of a nonresonance Zwanzig model and “quantum chaos”
Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 3, pp. 382-393
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the quantum dynamics of the Zwanzig model in the absence of resonance of an impurity site with a reservoir and obtain analytic expressions for the evolution of the impurity site population under different initial conditions. The agreement with numerical calculations is excellent. We analyze the possibility of the existence of quantum chaos in the model.
Keywords: Zwanzig model, quantum dynamics, quantum chaos. 
@article{TMF_2014_180_3_a6,
     author = {V. N. Likhachev and T. Yu. Astakhova and G. A. Vinogradov},
     title = {Exact solution of a~nonresonance {Zwanzig} model and {\textquotedblleft}quantum chaos{\textquotedblright}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {382--393},
     year = {2014},
     volume = {180},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a6/}
}
TY  - JOUR
AU  - V. N. Likhachev
AU  - T. Yu. Astakhova
AU  - G. A. Vinogradov
TI  - Exact solution of a nonresonance Zwanzig model and “quantum chaos”
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2014
SP  - 382
EP  - 393
VL  - 180
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a6/
LA  - ru
ID  - TMF_2014_180_3_a6
ER  - 
%0 Journal Article
%A V. N. Likhachev
%A T. Yu. Astakhova
%A G. A. Vinogradov
%T Exact solution of a nonresonance Zwanzig model and “quantum chaos”
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2014
%P 382-393
%V 180
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a6/
%G ru
%F TMF_2014_180_3_a6
V. N. Likhachev; T. Yu. Astakhova; G. A. Vinogradov. Exact solution of a nonresonance Zwanzig model and “quantum chaos”. Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 3, pp. 382-393. http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a6/

[1] R. Zwanzig, Lect. Theor. Phys., 3 (1960), 106–141

[2] N. A. Viglin, V. V. Ustinov, V. V. Osipov, Pisma v ZhETF, 86:3 (2007), 221–225 | DOI | MR

[3] V. A. Benderskii, L. N. Gak, E. I. Kats, ZhETF, 135:1 (2009), 176–193 | DOI

[4] V. A. Benderskii, L. N. Gak, E. I. Kats, ZhETF, 136:3 (2009), 589–600 | DOI

[5] K. E. Augustyn, J. C. Genereux, J. K. Barton, Angew. Chem. Int. Ed., 46:30 (2007), 5731–5733 | DOI

[6] J. K. Barton, E. D. Olmon, P. A. Sontz, Coord. Chem. Rev., 255:7–8 (2011), 619–634 | DOI

[7] S. S. Mallajosyula, S. K. Pati, J. Phys. Chem. Lett., 1:12 (2010), 1881–1894 | DOI

[8] B. Giese, Annu. Rev. Biochem., 71 (2002), 51–70 | DOI

[9] J. C. Genereux, J. K. Barton, Chem. Rev., 110:3 (2010), 1642–1682 | DOI

[10] T. Yu. Astakhova, V. N. Likhachev, G. A. Vinogradov, Uspekhi khimii, 81:11 (2012), 994–1010 | DOI

[11] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1963 | MR | Zbl

[12] G. M. Zaslavskii, R. Z. Sagdeev, Vvedenie v nelineinuyu fiziku. Ot mayatnika do turbulentnosti i khaosa, Nauka, M., 1988 | MR | Zbl

[13] F. M. Izrailev, Phys. Rep., 196:5–6 (1990), 299–392 | DOI | MR

[14] Ya. G. Sinai, Phys. A, 163:1 (1990), 197–204 | DOI | MR | Zbl

[15] P. V. Elyutin, UFN, 155:3 (1988), 397–442 | DOI | MR

[16] J. Ford, M. Ilg, Phys. Rev. A, 45:9 (1992), 6165–6173 | DOI

[17] J. P. Keating, M. Novaes, S. D. Prado, M. Sieber, Phys. Rev. Lett., 97:15 (2006), 150406, 4 pp. | DOI

[18] W. E. Bies, E. J. Heller, J. Phys. A, 35:27 (2002), 5673–5685 | DOI | MR | Zbl

[19] A. Backer, R. Schubert, J. Phys. A, 35:3 (2002), 539–564 | DOI | MR | Zbl

[20] F. Shtainer, Nelineinaya dinam., 2:2 (2006), 214–235