Abstract
It is proved for fermi systems that each translationally invariant state ω with square integrable correlation functions approaches a limit under the free time evolution. The limit state is the gauge invariant quasi-free state with the same two-point function as ω and it is characterized by a maximum entropy principle. Various properties of the limit are discussed, and the extension of the results to bose systems is also given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Robinson, D. W.: Commun. math. Phys.7, 337 (1968).
Lanford, O. E.: Commun. math. Phys.9, 176 (1968).
Sinai, Y., Volkoviskij, K.: (Unpublished).
de Pazzis, O.: (To be published).
Haag, R., Kadison, R., Kastler, D.: (Unpublished).
—— Systèmes à un nombre infini de degrés de Liberté CNRS. C.N.R.S. (Paris) (1970).
Ruelle, D.: Statistical mechanics. New York: Benjamin 1969.
Lanford, O. E., Robinson, D. W.: J. Math. Phys.9, 1120 (1968).
Ginibre, J.: J. Math. Phys.6, 252 (1965).
Lanford, O. E., Ruelle, D.: J. Math. Phys.8, 1460 (1967).
Araki, H., Lieb, E.: Commun. math. Phys.
Miracle-Sole, S., Robinson, D. W.: Commun. math. Phys.14, 235 (1969).
Robinson, D. W.: (Unpublished).
Lanford, O. E., Robinson, D. W.: (To be published).
Verbeure, A.: Cargèse lectures in physics (1969). New York: Gordon & Breach 1970.
Courbage, M., Miracle-Sole, S., Robinson, D. W.: Ann. Henri Poincaré, vol. XIV.2, 171 (1971).
Haag, R., Hugenholtz, N. M., Winnink, M.: Commun. math. Phys.5, 215 (1967).
Author information
Authors and Affiliations
Additional information
Alfred P. Sloan Foundation Fellow; on leave from Department of Mathematics, University of California, Berkeley, California (USA).
Rights and permissions
About this article
Cite this article
Lanford, O.E., Robinson, D.W. Approach to equilibrium of free quantum systems. Commun.Math. Phys. 24, 193–210 (1972). https://doi.org/10.1007/BF01877712
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01877712