Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2005-04-08
AIP Conference Proceedings Vol. {\bf 777} (2005) p.180, V. Zelevinsky (ed.).
Physics
Nuclear Physics
Nuclear Theory
8 pages, 4 figures. Lecture delivered at the workshop ``Nuclei and Mesoscopic Physics'', NSCL MSU, USA, October 23-26, 2004. T
Scientific paper
10.1063/1.1996884
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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