Anharmonic Chain with Lennard-Jones Interaction
About: This article is published in Physical Review A.The article was published on 1970-11-01. It has received 106 citations till now.
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01 Oct 1973
TL;DR: The term soliton has been coined to describe a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed.
Abstract: The term soliton has recently been coined to describe a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed. To date at least seven distinct wave systems, representing a wide range of applications in applied science, have been found to exhibit such solutions. This review paper covers the current status of soliton research, paying particular attention to the very important "inverse method" whereby the initial value problem for a nonlinear wave system can be solved exactly through a succession of linear calculations.
1,326 citations
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01 Jan 1969
TL;DR: In this paper, the authors discuss how statistical concepts enter the treatment of deterministic mechanical systems, with particular reference to trajectory instabilities and to the KAM theorem, and deal with large systems: the thermodynamic limit and the theory of infinite systems.
Abstract: Developments in the foundations of statistical mechanics during the past ten years or so. The author discusses how statistical concepts enter the treatment of deterministic mechanical systems, with particular reference to trajectory instabilities and to the KAM theorem. Then he deals with large systems: the thermodynamic limit and the theory of infinite systems. Non-equilibrium statistical mechanics is covered but LC relativistic statistical mechanics is not.
367 citations
TL;DR: In this paper, a brief review of the Fermi-pasta-Ulam paradox is given, together with its suggested resolutions and its relation to other physical problems, focusing on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective.
Abstract: A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection with the problems of ergodicity, integrability, chaos and stability of motion. New directions related to the Bose-Einstein condensation and quantum systems of interacting Bose-particles are also considered.
280 citations
TL;DR: In this paper, an extended concept of quantum ergodicity is proposed for relaxation processes in isolated molecules, and it allows straightforward numerical investigation of molecular models, such as triatomic models and linear molecules with four atoms.
Abstract: Recent advances in classical ergodic theory have produced qualitative information about the dynamics of anharmonic systems that is relevant to internal molecular dynamics and to unimolecular reaction rate theories. We describe here the results of an attempt to translate this progress into quantum molecular dynamics. Existing theories of quantum ergodicity are found to be ill suited to our task, so an extended concept of quantum ergodicity closely adhering to the well established classical concept is suggested. The new concept has the desired relevance to relaxation processes in isolated molecules, and it allows straightforward numerical investigation of molecular models. We report results for several triatomic models and one model of a linear molecule with four atoms. A prevalence of nonergodic behavior is observed for energies below the minimum required for dissociation.
174 citations
14 Mar 2007
106 citations