Exclusion statistics for particles with a discrete spectrum
We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the sta...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-11-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321321002704 |
| _version_ | 1819031105600225280 |
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| author | Stéphane Ouvry Alexios P. Polychronakos |
| author_facet | Stéphane Ouvry Alexios P. Polychronakos |
| author_sort | Stéphane Ouvry |
| collection | DOAJ |
| description | We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a relation with the Ramanujan continued fraction identity and appropriate generalizations. |
| first_indexed | 2024-12-21T06:40:46Z |
| format | Article |
| id | doaj.art-adf333b589c347bdb456bea8acc8b812 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-21T06:40:46Z |
| publishDate | 2021-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-adf333b589c347bdb456bea8acc8b8122022-12-21T19:12:42ZengElsevierNuclear Physics B0550-32132021-11-01972115573Exclusion statistics for particles with a discrete spectrumStéphane Ouvry0Alexios P. Polychronakos1LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France; Corresponding author.Department of Physics, City College of New York and the Graduate Center of CUNY, New York, NY 10038, USAWe formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a relation with the Ramanujan continued fraction identity and appropriate generalizations.http://www.sciencedirect.com/science/article/pii/S0550321321002704 |
| spellingShingle | Stéphane Ouvry Alexios P. Polychronakos Exclusion statistics for particles with a discrete spectrum Nuclear Physics B |
| title | Exclusion statistics for particles with a discrete spectrum |
| title_full | Exclusion statistics for particles with a discrete spectrum |
| title_fullStr | Exclusion statistics for particles with a discrete spectrum |
| title_full_unstemmed | Exclusion statistics for particles with a discrete spectrum |
| title_short | Exclusion statistics for particles with a discrete spectrum |
| title_sort | exclusion statistics for particles with a discrete spectrum |
| url | http://www.sciencedirect.com/science/article/pii/S0550321321002704 |
| work_keys_str_mv | AT stephaneouvry exclusionstatisticsforparticleswithadiscretespectrum AT alexiosppolychronakos exclusionstatisticsforparticleswithadiscretespectrum |