Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus

Lacroix, Denis; Ayik, Sakir

doi:10.1103/PhysRevC.101.014310

Title: 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 super-fluid 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, super-fluid 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:

Lacroix, Denis ^[1];

^[2]

Univ. Paris-Saclay, Orsay Cedex (France)
Tennessee Technological Univ., Cookeville, TN (United States)

Publication Date:: Mon Jan 13 00:00:00 EST 2020

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 2469-9985

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.

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                    Lacroix, Denis, & Ayik, Sakir. Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus.  United States.  https://doi.org/10.1103/PhysRevC.101.014310

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                    Lacroix, Denis, and Ayik, Sakir. Mon .  
"Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus".  United States.  https://doi.org/10.1103/PhysRevC.101.014310.  https://www.osti.gov/servlets/purl/1593774.

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@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 super-fluid 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, super-fluid 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         = {Mon Jan 13 00:00:00 EST 2020},

  month        = {Mon Jan 13 00:00:00 EST 2020}

}

Copy to clipboard

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Title: Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus

Abstract

Citation Formats

Nuclear Superfluidity book, August 2009

Gauge angle dependence in time-dependent Hartree-Fock-Bogoliubov calculations of O 20 + O 20 head-on collisions with the Gogny interaction journal, July 2016

Microscopic description of pair transfer between two superfluid Fermi systems: Combining phase-space averaging and combinatorial techniques journal, March 2018

Projection of good quantum numbers for reaction fragments journal, September 2019

The canonical form of an antisymmetric tensor and its application to the theory of superconductivity journal, December 1962

Particle-number restoration within the energy density functional formalism: Nonviability of terms depending on noninteger powers of the density matrices journal, April 2009

Density correlations in ultracold atomic Fermi gases journal, June 2007

Short range correlations and the isospin dependence of nuclear correlation functions journal, October 2018

Short-range correlations and the charge density journal, March 2019

Particle Transfer Reactions with the Time-Dependent Hartree-Fock Theory Using a Particle Number Projection Technique journal, November 2010

Time-dependent Hartree-Fock calculations for multinucleon transfer and quasifission processes in the Ni 64 + U 238 reaction journal, May 2016

Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices journal, October 2011

Microscopic description of pair transfer between two superfluid Fermi systems. II. Quantum mixing of time-dependent Hartree-Fock-Bogolyubov trajectories journal, June 2019

Considerations on the Flow of Superfluid Helium journal, April 1966

Projection in the occupation-number space and the canonical transformation journal, January 1970

Number of particles in fission fragments journal, August 2019

Self-consistent mean-field models for nuclear structure journal, January 2003

Probing Pair-Correlated Fermionic Atoms through Correlations in Atom Shot Noise journal, March 2005

Effect of pairing on one- and two-nucleon transfer below the Coulomb barrier: A time-dependent microscopic description journal, January 2013

Generalized virial theorem and pressure relation for a strongly correlated Fermi gas journal, December 2008

Suppression of Density Fluctuations in a Quantum Degenerate Fermi Gas journal, July 2010

Suppressed fluctuations in Fermi gases journal, July 2010

Local Observation of Antibunching in a Trapped Fermi Gas journal, July 2010

Large momentum part of a strongly correlated Fermi gas journal, December 2008

Novel Role of Superfluidity in Low-Energy Nuclear Reactions journal, July 2017

Energetics of a strongly correlated Fermi gas journal, December 2008

Fluctuations of the number of particles within a given volume in cold quantum gases journal, December 2007

Normal Forms of Complex Matrices journal, September 1962

Examining empirical evidence of the effect of superfluidity on the fusion barrier journal, April 2018

Particle-number restoration within the energy density functional formalism journal, April 2009

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels journal, April 2009

Particle transfer reactions with the time-dependent Hartree-Fock theory using a particle number projection technique text, January 2010

Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices text, January 2010

Local atom-number fluctuations in quantum gases at finite temperature text, January 2011

Symmetry restoration in Hartree-Fock-Bogoliubov based theories text, January 2011

Effect of pairing on one- and two-nucleon transfer below the Coulomb barrier: a time-dependent microscopic description text, January 2012

Examining empirical evidence of the effect of superfluidity on the fusion barrier text, January 2018

Short-range correlations and the charge density text, January 2018

Microscopic description of pair transfer between two superfluid systems (II): a quantum mixing of Time-Dependent Hartree-Fock Bogolyubov trajectories text, January 2019

Energetics of a strongly correlated Fermi gas text, January 2005

Nuclear Superfluidity
book, August 2009

Gauge angle dependence in time-dependent Hartree-Fock-Bogoliubov calculations of ${}^{20}O + {}^{20}O$ head-on collisions with the Gogny interaction
journal, July 2016

Microscopic description of pair transfer between two superfluid Fermi systems: Combining phase-space averaging and combinatorial techniques
journal, March 2018

Projection of good quantum numbers for reaction fragments
journal, September 2019

The canonical form of an antisymmetric tensor and its application to the theory of superconductivity
journal, December 1962

Particle-number restoration within the energy density functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
journal, April 2009

Density correlations in ultracold atomic Fermi gases
journal, June 2007

Short range correlations and the isospin dependence of nuclear correlation functions
journal, October 2018

Short-range correlations and the charge density
journal, March 2019

Particle Transfer Reactions with the Time-Dependent Hartree-Fock Theory Using a Particle Number Projection Technique
journal, November 2010

Time-dependent Hartree-Fock calculations for multinucleon transfer and quasifission processes in the ${}^{64}{Ni} + {}^{238}U$ reaction
journal, May 2016

Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices
journal, October 2011

Microscopic description of pair transfer between two superfluid Fermi systems. II. Quantum mixing of time-dependent Hartree-Fock-Bogolyubov trajectories
journal, June 2019

Considerations on the Flow of Superfluid Helium
journal, April 1966

Projection in the occupation-number space and the canonical transformation
journal, January 1970

Number of particles in fission fragments
journal, August 2019

Self-consistent mean-field models for nuclear structure
journal, January 2003

Probing Pair-Correlated Fermionic Atoms through Correlations in Atom Shot Noise
journal, March 2005

Effect of pairing on one- and two-nucleon transfer below the Coulomb barrier: A time-dependent microscopic description
journal, January 2013

Generalized virial theorem and pressure relation for a strongly correlated Fermi gas
journal, December 2008

Suppression of Density Fluctuations in a Quantum Degenerate Fermi Gas
journal, July 2010

Suppressed fluctuations in Fermi gases
journal, July 2010

Local Observation of Antibunching in a Trapped Fermi Gas
journal, July 2010

Large momentum part of a strongly correlated Fermi gas
journal, December 2008

Novel Role of Superfluidity in Low-Energy Nuclear Reactions
journal, July 2017

Energetics of a strongly correlated Fermi gas
journal, December 2008

Fluctuations of the number of particles within a given volume in cold quantum gases
journal, December 2007

Normal Forms of Complex Matrices
journal, September 1962

Examining empirical evidence of the effect of superfluidity on the fusion barrier
journal, April 2018

Particle-number restoration within the energy density functional formalism
journal, April 2009

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels
journal, April 2009

Particle transfer reactions with the time-dependent Hartree-Fock theory using a particle number projection technique
text, January 2010

Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices
text, January 2010

Local atom-number fluctuations in quantum gases at finite temperature
text, January 2011

Symmetry restoration in Hartree-Fock-Bogoliubov based theories
text, January 2011

Effect of pairing on one- and two-nucleon transfer below the Coulomb barrier: a time-dependent microscopic description
text, January 2012

Examining empirical evidence of the effect of superfluidity on the fusion barrier
text, January 2018

Short-range correlations and the charge density
text, January 2018

Microscopic description of pair transfer between two superfluid systems (II): a quantum mixing of Time-Dependent Hartree-Fock Bogolyubov trajectories
text, January 2019

Energetics of a strongly correlated Fermi gas
text, January 2005