Maier, Georg and Echter, Carolyn and Urbina, Juan Diego and Lewenkopf, Caio and Richter, Klaus (2025) Ensemble-averaged mean-field many-body level density: An indicator of integrable versus chaotic single-particle dynamics. PHYSICAL REVIEW E, 111 (5): 054202. ISSN 2470-0045, 2470-0053
Full text not available from this repository.Abstract
According to the quantum chaos paradigm, the nature of a system's classical dynamics, whether integrable or chaotic, is universally reflected in the fluctuations of its quantum spectrum. However, since many-body spectra in the mean-field limit are composed of independent single-particle energy levels, their spectral fluctuations always display Poissonian behavior and hence cannot be used to distinguish underlying chaotic from integrable singleparticle dynamics. We demonstrate that this distinction can, instead, be revealed from the mean many-body level density (at fixed energy) and its variance after averaging over ensembles representing different types of singleparticle dynamics. This is in strong contrast to the energy-averaged mean level density (of a given system) that is assumed not to carry such information and is routinely removed to focus on universal signatures. To support our claim we systematically analyze the role of single-particle level correlations, that enter through Poisson and random matrix statistics (of various symmetry classes) into the ensemble-averaged density of states and its variance, contrasting bosonic and fermionic many-body systems. Our analytical study, together with extensive numerical simulations for systems with N 5 particles consistently reveal significant differences (up to an order of magnitude for fermions and even larger for bosons) in the mean many-body level densities, depending on the nature of the underlying dynamics. Notably, in the fermionic case Poisson-type single-particle level fluctuations precisely cancel contributions from indistinguishability, such that the average many-body spectral density equals the (Thomas-Fermi) volume term. We further highlight the difference between the mean level density and its variance as functions of the total energy E and the excitation energy Q.
| Item Type: | Article |
|---|---|
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 16 Jul 2026 06:50 |
| Last Modified: | 16 Jul 2026 06:50 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66355 |
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