Abstract
The response, relaxation and correlation functions are defined for any vector state ε of a von Neumann algebra\(\mathfrak{M}\), acting on a Hilbert space ℋ, satisfying the KMS-condition. An operator representation of these functions is given on a particular Hilbert space
.
With this technique we prove the existence of the static admittance and the relaxation function. Finally we generalize the fluctuation-dissipation theorem and other relations between the above mentionned functions to infinite systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Haag, R., Hugenholtz, N. M., Winnink, M.: Commun. math. Phys.5, 215 (1967)
Haake, F.: Statistical treatment of open systems by generalized master equations. Springer Tracts in Modern Physics, Vol. 66. Berlin-Heidelberg-New York: springer 1973
Prigogine, I.: The statistical interpretation of non-equilibrium entropy. In: The Boltzman equation, theory and applications. Cohen, E.G.D., Thirring, W., eds., Berlin-Heidelberg-New York: Springer 1973
Bongaarts, P. J. M., Fannes, M., Verbeure, A.: Physica68, 587 (1973)
Davies, E. B.: Markovian master equations; to appear in Comm. Math. Phys.
Presutti, E., Scacciatelli, E., Sewell, G. S., Wanderlingh, F.: J. Math. Phys.13, 1085 (1972)
Hepp, K., Lieb, E. H.: Helv. Phys. Acta46, 573 (1973)
Robinson, D. W.:C*-algebras and quantum statistical mechanics; Lecture given at the Varenna Summer School onC*-algebras (1973)
Haag, R., Kaster, D., Trych-Pohlmeyer, E.: commun. math. Phys.38, 173 (1974)
Kubo, R.: J. Phys. Soc. Japan12, 570 (1957)
Mori, H.: Progr. Theor. Phys.33, 423 (1965)
Takesaki, M.: Tomita's theory of modular Hilbert algebras and its applications; Lecture Notes in Mathematics128. Berlin-Heidelberg-New York: Springer 1970
Dunford, N., Schwartz, J. T.: Linear operators, Part II. London: Interscience Publishers 1963
Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966
Balslev, E.: Spectral theory of Schrödinger operators of Many-Body systems. Lecture Notes. University of Leuven, Belgium 1971
Van Daele, A.: J. Funct. Ann.15, 378 (1974)
Bogoliubov, N. M.: Dubna reports (unpublished); Physik. Abhandl. Sowjet Union6, 1; 113–229 (1962)
Ruelle, D.: Statistical mechanics. Lemma 5.5. New York: W. A. Benjamin, Inc. 1969
Stone, M. H.: Linear transformations in Hilbert space and their applications to analysis. Providence. Amm. Math. Soc. Colloq. Publ. Vol.15 (1932)
Verbeure, A., Weder, R. A.: Stability in linear response and clustering properties. Commun. math. Phys.44, 101–105 (1975)
Author information
Authors and Affiliations
Additional information
Communicated by J. L. Lebowitz
Rights and permissions
About this article
Cite this article
Naudts, J., Verbeure, A. & Weder, R. Linear response theory and the KMS condition. Commun.Math. Phys. 44, 87–99 (1975). https://doi.org/10.1007/BF01609060
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01609060