Approach to equilibrium of statistical systems: classical particles and quantum fields off-equilibrium
Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bat...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/102714 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/102714 |
| Access Level: | acceso abierto |
| Palabra clave: | 53 Statistical systems Classical particles Quantum fields Approach to equilibrium Física (Física) 2212 Física Teórica |
| Sumario: | Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bath (ℎ), is described by the non-equilibrium reversible Liouville distribution (W) and equation, with a suitable initial condition. The Boltzmann equilibrium distribution _() generates orthogonal (Hermite) polynomials _() in momenta. Suitable moments _() of W (using the _()’s) yield a non-equilibrium three-term hierarchy (different from the standard Bogoliubov–Born–Green–Kirkwood–Yvon one), solved through operator continued fractions. After a long-t approximation, the _()’s yield irreversibly approach to equilibrium. The approach is extended (without ℎ) to: (i) a non-equilibrium system of N classical non-relativistic particles interacting through repulsive short range potentials and (ii) a classical ^(4) field theory (without ℎ). The extension to one non-relativistic quantum particle (with ℎ) employs the non-equilibrium Wigner function (_()): difficulties related to non-positivity of _() are bypassed so as to formulate approximately approach to equilibrium. A non-equilibrium quantum anharmonic oscillator is analyzed differently, through functional integral methods. The latter allows an extension to relativistic quantum ^(4) field theory (a meson gas off-equilibrium, without ℎ), facing ultraviolet divergences and renormalization. Genuine simplifications of quantum ^(4) theory at high T and large distances and long t occur; then, through a new argument for the field-theoretic case, the theory can be approximated by a classical ^(4) one, yielding an approach to equilibrium. |
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