Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus
Abstract
Here, we analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator techniques directly linked to the characteristic function of the probability distribution. The method is illustrated in atomic nuclei. The nature of the particle number fluctuations from small to large volumes compared to the system size is carefully analyzed in three cases: normal systems, superfluid systems and super fluid systems with total number restoration. The transition from Poissonian distribution in the small volume limit to Gaussian fluctuations as the number of particles participating to the fluctuations increases is analyzed both in the interior and at the surface of the system. Lastly, while the restoration of the total number of particles is not necessary for small volume, we show that it affects the counting statistics as soon as more than a very few particles are involved.
 Authors:

 Univ. ParisSaclay, Orsay Cedex (France)
 Tennessee Technological Univ., Cookeville, TN (United States)
 Publication Date:
 Research Org.:
 Tennessee Technological Univ., Cookeville, TN (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP)
 OSTI Identifier:
 1593774
 Grant/Contract Number:
 SC0015513
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 101; Journal Issue: 1; Journal ID: ISSN 24699985
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Nuclear density functional theory; Nucleon distribution
Citation Formats
Lacroix, Denis, and Ayik, Sakir. Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus. United States: N. p., 2020.
Web. doi:10.1103/PhysRevC.101.014310.
Lacroix, Denis, & Ayik, Sakir. Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus. United States. doi:10.1103/PhysRevC.101.014310.
Lacroix, Denis, and Ayik, Sakir. Mon .
"Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus". United States. doi:10.1103/PhysRevC.101.014310. https://www.osti.gov/servlets/purl/1593774.
@article{osti_1593774,
title = {Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus},
author = {Lacroix, Denis and Ayik, Sakir},
abstractNote = {Here, we analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator techniques directly linked to the characteristic function of the probability distribution. The method is illustrated in atomic nuclei. The nature of the particle number fluctuations from small to large volumes compared to the system size is carefully analyzed in three cases: normal systems, superfluid systems and super fluid systems with total number restoration. The transition from Poissonian distribution in the small volume limit to Gaussian fluctuations as the number of particles participating to the fluctuations increases is analyzed both in the interior and at the surface of the system. Lastly, while the restoration of the total number of particles is not necessary for small volume, we show that it affects the counting statistics as soon as more than a very few particles are involved.},
doi = {10.1103/PhysRevC.101.014310},
journal = {Physical Review C},
number = 1,
volume = 101,
place = {United States},
year = {2020},
month = {1}
}
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