dorsal/arxiv
View SchemaLevel density of a Fermion gas: average growth, fluctuations, universality
| Authors | Patricio Leboeuf |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0504026 |
| URL | https://arxiv.org/abs/nucl-th/0504026 |
| DOI | 10.1063/1.1996884 |
| Journal | AIP Conference Proceedings Vol. {\bf 777} (2005) p.180, V. Zelevinsky (ed.). |
Abstract
It has been shown by H. Bethe more than 70 years ago that the number of excited states of a Fermi gas grows, at high excitation energies $Q$, like the exponential of the square root of $Q$. This result takes into account only the average density of single particle (SP) levels near the Fermi energy. It ignores two important effects, namely the discreteness of the SP spectrum, and its fluctuations. We show that the discreteness of the SP spectrum gives rise to smooth finite--$Q$ corrections. Mathematically, these corrections are associated to the problem of partitions of an integer. On top of the smooth growth of the many--body density of states there are, generically, oscillations. An explicit expression of these oscillations is given. Their properties strongly depend on the regular or chaotic nature of the SP motion. In particular, we analyze their typical size, temperature dependence and probability distribution, with emphasis on their universal aspects.
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"abstract": "It has been shown by H. Bethe more than 70 years ago that the number of\nexcited states of a Fermi gas grows, at high excitation energies $Q$, like the\nexponential of the square root of $Q$. This result takes into account only the\naverage density of single particle (SP) levels near the Fermi energy. It\nignores two important effects, namely the discreteness of the SP spectrum, and\nits fluctuations. We show that the discreteness of the SP spectrum gives rise\nto smooth finite--$Q$ corrections. Mathematically, these corrections are\nassociated to the problem of partitions of an integer. On top of the smooth\ngrowth of the many--body density of states there are, generically,\noscillations. An explicit expression of these oscillations is given. Their\nproperties strongly depend on the regular or chaotic nature of the SP motion.\nIn particular, we analyze their typical size, temperature dependence and\nprobability distribution, with emphasis on their universal aspects.",
"arxiv_id": "nucl-th/0504026",
"authors": [
"Patricio Leboeuf"
],
"categories": [
"nucl-th",
"cond-mat.stat-mech"
],
"doi": "10.1063/1.1996884",
"journal_ref": "AIP Conference Proceedings Vol. {\\bf 777} (2005) p.180, V.\n Zelevinsky (ed.).",
"title": "Level density of a Fermion gas: average growth, fluctuations, universality",
"url": "https://arxiv.org/abs/nucl-th/0504026"
},
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