Abstract
We prove the existence of a time evolution for infinite anharmonic crystals for a large class of initial configurations. When there are strong forces tying particles to their equilibrium positions then the class of permissible initial conditions can be specified explicitly; otherwise it can only be shown to have full measure with respect to the appropriate Gibbs state. Uniqueness of the time evolution is also proven under suitable assumptions on the solutions of the equations of motion.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
O. E. Lanford III, Commun. Math. Phys. 11: 257 (1969).
O. E. Lanford III, Commun. Math. Phys. 11: 257 (1969).
O. E. Lanford III and J. L. Lebowitz, in Lecture Notes in Physics, No. 38, Springer-Verlag (1975), p. 144; J. L. van Hemmen, Thesis, University of Groningen (1976).
O. E. Lanford III, in Lecture Notes in Physics, No. 38, Springer-Verlag (1975), p. 1.
Ya. G. Sinai, Vestnik Markov. Univ. Ser. I, Math. Meh. 1974: 152.
C. Marchioro, A. Pellegrinotti, and E. Presutti, Commun. Math. Phys. 40: 175 (1975).
N. W. Ashcroft and N. D. Mermin, Solid State Physics, Holt, Rinehart and Winston (1976).
H. J. Brascamp, E. H. Lieb, and J. L. Lebowitz, The Statistical Mechanics of Anharmonic Lattices, in Proceedings of the 40th Session of the International Statistics Institute, Warsaw (1975).
D. Ruelle, Commun. Math. Phys. 50: 189 (1976).
J. L. Lebowitz and E. Presutti, Commun. Math. Phys. 50: 195 (1976).
L. Breiman, Probability, Addison-Wesley, Section 3. 14.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1977 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lanford, O.E., Lebowitz, J.L., Lieb, E.H. (1977). Time Evolution of Infinite Anharmonic Systems. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Statistical Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10018-9_23
Download citation
DOI: https://doi.org/10.1007/978-3-662-10018-9_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-06092-2
Online ISBN: 978-3-662-10018-9
eBook Packages: Springer Book Archive