Operator Algebras and Quantum Statistical Mechanics: Equilibrium States Models in Quantum Statistical Mechanics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1981
|
| Schriftenreihe: | Texts and Monographs in Physics
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this chapter, and the following one, we examine various applications of C*-algebras and their states to statistical mechanics. Principally we analyze the structural properties of the equilibrium states of quantum systems consisting of a large number of particles. In Chapter 1 we argued that this leads to the study of states of infinite-particle systems as an initial approximation. There are two approaches to this study which are to a large extent complementary. The first approach begins with the specific description of finite systems and their equilibrium states provided by quantum statistical mechanics. One then rephrases this description in an algebraic language which identifies the equilibrium states as states over a quasi-local C*-algebra generated by subalgebras corresponding to the observables of spatial subsystems. Finally, one attempts to calculate an approximation of these states by taking their limit as the volume of the system tends to infinity, the so-called thermodynamic limit. The infinite-volume equilibrium states obtained in this manner provide the data for the calculation of bulk properties of the matter under consideration as functions of the thermodynamic variables. By this we mean properties such as the particle density, or specific heat, as functions of the temperature and chemical potential, etc. In fact, the infinite-volume data provides a much more detailed, even microscopic, description of the equilibrium phenomena although one is only generally interested in the bulk properties and their fluctuations |
| Beschreibung: | 1 Online-Ressource (XI, 507 p) |
| ISBN: | 9783662090893 9783662090916 |
| ISSN: | 1864-5879 |
| DOI: | 10.1007/978-3-662-09089-3 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:20:55Z |
| institution | BVB |
| isbn | 9783662090893 9783662090916 |
| issn | 1864-5879 |
| language | English |
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| physical | 1 Online-Ressource (XI, 507 p) |
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| publishDate | 1981 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Texts and Monographs in Physics |
| spelling | Bratteli, Ola Verfasser aut Operator Algebras and Quantum Statistical Mechanics Equilibrium States Models in Quantum Statistical Mechanics by Ola Bratteli, Derek W. Robinson Berlin, Heidelberg Springer Berlin Heidelberg 1981 1 Online-Ressource (XI, 507 p) txt rdacontent c rdamedia cr rdacarrier Texts and Monographs in Physics 1864-5879 In this chapter, and the following one, we examine various applications of C*-algebras and their states to statistical mechanics. Principally we analyze the structural properties of the equilibrium states of quantum systems consisting of a large number of particles. In Chapter 1 we argued that this leads to the study of states of infinite-particle systems as an initial approximation. There are two approaches to this study which are to a large extent complementary. The first approach begins with the specific description of finite systems and their equilibrium states provided by quantum statistical mechanics. One then rephrases this description in an algebraic language which identifies the equilibrium states as states over a quasi-local C*-algebra generated by subalgebras corresponding to the observables of spatial subsystems. Finally, one attempts to calculate an approximation of these states by taking their limit as the volume of the system tends to infinity, the so-called thermodynamic limit. The infinite-volume equilibrium states obtained in this manner provide the data for the calculation of bulk properties of the matter under consideration as functions of the thermodynamic variables. By this we mean properties such as the particle density, or specific heat, as functions of the temperature and chemical potential, etc. In fact, the infinite-volume data provides a much more detailed, even microscopic, description of the equilibrium phenomena although one is only generally interested in the bulk properties and their fluctuations Physics Mathematical physics Mathematical Methods in Physics Numerical and Computational Physics Mathematische Physik Robinson, Derek W. 1935- Sonstige (DE-588)107889455 oth https://doi.org/10.1007/978-3-662-09089-3 Verlag Volltext |
| spellingShingle | Bratteli, Ola Operator Algebras and Quantum Statistical Mechanics Equilibrium States Models in Quantum Statistical Mechanics Physics Mathematical physics Mathematical Methods in Physics Numerical and Computational Physics Mathematische Physik |
| title | Operator Algebras and Quantum Statistical Mechanics Equilibrium States Models in Quantum Statistical Mechanics |
| title_auth | Operator Algebras and Quantum Statistical Mechanics Equilibrium States Models in Quantum Statistical Mechanics |
| title_exact_search | Operator Algebras and Quantum Statistical Mechanics Equilibrium States Models in Quantum Statistical Mechanics |
| title_full | Operator Algebras and Quantum Statistical Mechanics Equilibrium States Models in Quantum Statistical Mechanics by Ola Bratteli, Derek W. Robinson |
| title_fullStr | Operator Algebras and Quantum Statistical Mechanics Equilibrium States Models in Quantum Statistical Mechanics by Ola Bratteli, Derek W. Robinson |
| title_full_unstemmed | Operator Algebras and Quantum Statistical Mechanics Equilibrium States Models in Quantum Statistical Mechanics by Ola Bratteli, Derek W. Robinson |
| title_short | Operator Algebras and Quantum Statistical Mechanics |
| title_sort | operator algebras and quantum statistical mechanics equilibrium states models in quantum statistical mechanics |
| title_sub | Equilibrium States Models in Quantum Statistical Mechanics |
| topic | Physics Mathematical physics Mathematical Methods in Physics Numerical and Computational Physics Mathematische Physik |
| topic_facet | Physics Mathematical physics Mathematical Methods in Physics Numerical and Computational Physics Mathematische Physik |
| url | https://doi.org/10.1007/978-3-662-09089-3 |
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