Relaxation times and ergodic properties in a realistic ionic-crystal model, and the modern form of the FPU problem
| Autor: | Andrea Carati, Luigi Galgani, Fabrizio Gangemi, Roberto Gangemi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Physics Work (thermodynamics) Statistical Mechanics (cond-mat.stat-mech) Open problem Ergodicity Fermi–Pasta–Ulam problem Classical Physics (physics.class-ph) FOS: Physical sciences Physics - Classical Physics Statistical mechanics Mathematical Physics (math-ph) Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Specific kinetic energy 0103 physical sciences Ergodic theory Statistical physics Relaxation (approximation) 010306 general physics Relaxation times Ergodicity Ionic crystal model Long-range interactions FPU problem Condensed Matter - Statistical Mechanics Mathematical Physics |
| Popis: | It is well known that Gibbs’ statistical mechanics is not justified for systems presenting long-range interactions, such as plasmas or galaxies. In a previous work we considered a realistic FPU-like model of an ionic crystal (and thus with long-range interactions), and showed that it reproduces the experimental infrared spectra from 1000 K down to 7 K, provided one abandons the Gibbs identification of temperature in terms of specific kinetic energy, at low temperatures. Here we investigate such a model in connection with its ergodic properties. The conclusion we reach is that at low temperatures ergodicity does not occur, and thus the Gibbs prescriptions are not dynamically justified, up to geological time scales. We finally give a preliminary result indicating how the so-called “nonclassical” q-statistics show up in the realistic ionic-crystal model. How to formulate a consistent statistical mechanics, with the corresponding suitable identification of temperature in such nonergodicity conditions, remains an open problem, which apparently constitutes the modern form of the FPU problem. |
| Databáze: | OpenAIRE |
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