Geodesic
Convergence to an equilibrium state for a~one-dimensional quantum system of hard rods
Izvestiya. Mathematics , Tome 21 (1983) no. 3, pp. 547-583.

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In this paper a theorem is proved on the convergence to an equilibrium state during the course of the time evolution of an infinite, one-dimensional system of quantum particles interacting by means of a “hard-rod” potential. The basic idea consists in the reduction of the time evolution of the system of hard rods to the time evolution of free particles. The case of free motion was studied earlier by O. Lanford and D. Robinson. Bibliography: 23 titles. 
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Yu. M. Sukhov. Convergence to an equilibrium state for a~one-dimensional quantum system of hard rods. Izvestiya. Mathematics , Tome 21 (1983) no. 3, pp. 547-583. http://geodesic.mathdoc.fr/item/IM2_1983_21_3_a5/

[1] Dubin D. A., Solvable models in algebraic statistical mechanics, Clarendon Press, 1974

[2] Emch G. G., Algebraic methods in statistical mechanics and quantum field theory, Wiley-Interscience, 1972 ; Emkh G. G., Algebraicheskie metody v statisticheskoi mekhanike i kvantovoi teorii polya, Mir, M., 1976 | Zbl

[3] Bratteli O., Robinson D. W., Operator algebras and quantum statistical mechanics. 1, Springer-Verlag, 1979 ; Brattelli O., Robinson D., Mir, M., 1982 ; 2, Springer-Verlag, 1981 | MR | Zbl | MR

[4] Dobrushin R. L., Sukhov Yu. M., “Vremennaya asimptotika dlya nekotorykh vyrozhdennykh modelei evolyutsii sistem s beskonechnym chislom chastits”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat., 14, VINITI AN SSSR, M., 1979, 147–254 | MR

[5] Boldrighini C., Dobrushin R. L., Suhov Yu. M., Time asymptotics for some degenerate models of the evolution of systems with infinitely many particles, preprint, Camerino University (Italy), 1980

[6] Rocca F., Sirugue M., Testard D., “On a class of equilibrium states under the Kubo–Martin–Schwinger condition. I. Fermions”, Comm. Math. Phys., 13 (1969), 317–334 | DOI | MR

[7] Rocca F., Sirugue M., Testard D., “On a class of equilibrium states under the Kubo–Martin–Schwinger condition. II. Bosons”, Comm. Math. Phys., 19 (1970), 119–141 | DOI | MR

[8] Lanford O. E., Robinson D. W., “Approach to equilibrium of free quantum systems”, Commun. Math. Phys., 24 (1972), 193–210 | DOI | MR

[9] Prokhorov Yu. V., Rozanov Yu. A., Teoriya veroyatnostei, Nauka, M., 1972 | MR

[10] Ruelle D., Statistical Mechanics. Rigorous results, W. A. Benjamen, 1969 ; Ryuel D., Statisticheskaya mekhanika. Strogie rezultaty, Mir, M., 1972 | MR | Zbl

[11] Matthes K., Kerstan J., Mecke J., Infinitely divisible point processes, Wiley and Sons, N. Y., 1978 ; Mattes K., Kerstan I., Meke I., Bezgranichno delimye tochechnye protsessy, Nauka, M., 1981 | MR | Zbl

[12] Ibragimov I. A., Rozanov Yu. A., Gaussovskie sluchainye protsessy, Nauka, M., 1970 | MR

[13] Ibragimov I. A., Linnik Yu. V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965

[14] Malyshev V. A., “Klasternye razlozheniya v reshetchatykh modelyakh statisticheskoi fiziki i kvantovoi teorii polya”, Uspekhi matem. nauk, 35:2 (1980), 3–53 | MR

[15] Ginibre J., “Reduced density matrices of quantum gases. I”, J. Math. Phys., 6 (1965), 238–251 ; Zhinibr Zh., “Predelnye matritsy plotnosti kvantovykh gazov”, Matematika, 12:4 (1968), 104–130; “II”, J. Math. Phys., 6 (1965), 252–262 ; “III”, J. Math. Phys., 6 (1965), 1432–1446 | DOI | MR | Zbl | DOI | DOI

[16] Ginibre J., “Some applications of functional integration in statistical mechanics”, Statistical Mechanics and Quantum Field Theory (Les Houches Summer Schoof of Theoretical Physics), Gordon and Breach, 1970

[17] Novikov I. D., “Sostoyaniya Gibbsa v kvantovoi statisticheskoi fizike”, Funkts. analiz i ego prilozh., 4 (1970), 79–80

[18] Sukhov Yu. M., “Predelnye matritsy plotnosti dlya odnomernykh nepreryvnykh sistem kvantovoi statisticheskoi mekhaniki”, Matem. sb., 83 (1970), 491–512 | Zbl

[19] Sukhov Yu. M., “Regulyarnost predelnykh matrits plotnosti dlya odnomernykh nepreryvnykh kvantovykh sistem”, Trudy Mosk. matem. o-va, 26 (1972), 151–179 | Zbl

[20] Sukhov Yu. M., “Suschestvovanie i regulyarnost predelnogo sostoyaniya Gibbsa dlya odnomernykh nepreryvnykh sistem kvantovoi statisticheskoi mekhaniki”, Dokl. AN SSSR, 195:5 (1970), 1042–1044

[21] Suhov Yu. M., “Sur les systèmes continus de la Méchanique statistique quantique a une dimension avec une intéraction de portée infinie”, Compt. Rend. A. S. Paris (A279), 1974, 433–434 | MR

[22] Suhov Yu. M., “Limit Gibbs states for some classes of one dimensional systems of quantum statistical mechanics”, Commun. Math. Phys., 62 (1978), 119–136 | DOI | MR

[23] Dashyan Yu. R., “Ekvivalentnost malogo i bolshogo kanonicheskikh ansamblei Gibbsa dlya odnomernykh sistem kvantovoi statisticheskoi mekhaniki”, Teor. i matem. fizika, 34:3 (1978), 341–352 | MR