Abstract
We generalize the notion of a topological transitive or a topologically mixing system for quantum mechanical systems in a consistent way. We compare these ergodic properties with the classical results. We deal with some aspects of nearly Abelian systems and investigate some relations between these notions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. Bratteli and D. W. Robinson,Operator Algebras and Quantum Statistical Mechanics, Vol. 1 (Springer, New York, 1979).
S. Doplicher, D. Kastler, and E. Størmer, Invariant states and asymtotic abelianness,J.Funct. Anal. 3:419–434 (1969).
D. Kastler, M. Mebkhout, G. Loupias, and L. Michel, Central decomposition of invariant states, applications to the group of time translations and euclidean transformations in algebraic field theory,Commun. Math. Phys. 27:195–222 (1972).
G. K. Pederson,C*-Algebras and Their Automorphism Groups (Academic Press, London, 1979).
M. Reed and B. Simon,Fourier Analysis, Self-Adjointness (Academic Press, New York, 1975).
S. Sakai,C*-Algebras and W*-Algebras (Springer, New York, 1971).
M. Takesaki,J. Fund. Anal. 9:306–321 (1972).
W. Thirring,Quantenmechanik grosser Systeme. (Springer, Vienna, 1980).
P. Walters,An Introduction to Ergodic Theory (Springer, New York, 1982).
B. Weiss,Math. Syst. Theory 5:71–75 (1971).
H. Wiklicky, Über masstheoretische und topologische Vermischungsbegriffe, Master's thesis, Universität Wien, Vienna, (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Narnhofer, H., Thirring, W. & Wiklicky, H. Transitivity and ergodicity of quantum systems. J Stat Phys 52, 1097–1112 (1988). https://doi.org/10.1007/BF01019741
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01019741