On the One-Dimensional Transition State Theory and the Relation between Statistical and Deterministic Oscillation Frequencies of Anharmonic Energy Wells |
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Authors: | Stefano Giordano Fabrizio Cleri Ralf Blossey |
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Affiliation: | 1. CNRS, Centrale Lille, Univ. Polytechnique Hauts-de-France, UMR 8520 - IEMN - Institut d'Électronique, de Microélectronique et de Nanotechnologie, University of Lille, Lille, F-59000 France;2. Institut d'Électronique, de Microélectronique et de Nanotechnologie (IEMN CNRS UMR8520) and Departement de Physique, University of Lille, Villeneuve d'Ascq, F-59652 France;3. Unité de Glycobiologie Structurale et Fonctionnelle (UGSF), CNRS UMR8576 University of Lille, Lille, F-59000 France |
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Abstract: | The transition state theory allows the development of approximated models useful to study the non-equilibrium evolution of systems undergoing transformations between two states (e.g., chemical reactions). In a simplified 1D setting, the characteristic rate constants are typically written in terms of a temperature-dependent characteristic oscillation frequency , describing the exploration of the phase space. As a particular case, this statistical oscillation frequency can be defined for an arbitrary convex potential energy well. This value is compared here with the deterministic oscillation frequency of the corresponding anharmonic oscillator. It is proved that there is a universal relationship between statistical and deterministic frequencies, which is the same for classical and relativistic mechanics. The independence of this relationship from the adopted physical laws gives it an interesting thermodynamic and pedagogical meaning. Several examples clarify the meaning of this relationship from both physical and mathematical viewpoints. |
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Keywords: | anharmonic oscillator relativistic dynamics transition state theory |
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