Time evolution of infinite anharmonic systems

Oscar E. Lanford; Joel L. Lebowitz; Elliott H. Lieb

doi:10.1007/BF01152283

Time evolution of infinite anharmonic systems

Oscar E. Lanford, Joel L. Lebowitz, Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

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.

Original language	English (US)
Pages (from-to)	453-461
Number of pages	9
Journal	Journal of Statistical Physics
Volume	16
Issue number	6
DOIs	https://doi.org/10.1007/BF01152283
State	Published - Jun 1977

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Existence of time evolution
strong restoring forces
uniqueness

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10.1007/BF01152283

Cite this

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title = "Time evolution of infinite anharmonic systems",

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.",

keywords = "Existence of time evolution, strong restoring forces, uniqueness",

author = "Lanford, {Oscar E.} and Lebowitz, {Joel L.} and Lieb, {Elliott H.}",

year = "1977",

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AU - Lebowitz, Joel L.

AU - Lieb, Elliott H.

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N2 - 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.

AB - 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.

KW - Existence of time evolution

KW - strong restoring forces

KW - uniqueness

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ER -

Time evolution of infinite anharmonic systems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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