Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Generalized quantal distribution functions within factorization approach : Some general results for bosons and fermions

Diego F. Torres, Uǧur Tırnaklı

Published Jan 1, 1998• 23 citations
OpenAlex

Abstract

The generalized quantal distribution functions are investigated concerning systems of non-interacting bosons and fermions. The formulae for the number of particles and energy are presented and applications to the Chandrasekhar limit of white dwarfs stars and to the Bose-Einstein condensation are commented.

Related papers

Generalized quantal distribution functions within factorization approach: some general results for bosons and fermions

Diego F. Torres, Uǧur Tırnaklı

arXiv:cond-mat/9904098•Physica A Statistical Mechanics and its Applications•Dec 1, 1998•29 citations

Investigations on finite ideal quantum gases

Heinz–Jürgen Schmidt, Jürgen Schnack

Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to excited nuclei and Bose–Einstein condensation are discussed.

•Jan 1, 1998•17 citations

Exact quantum solutions of extraordinary N -body problems

D. Lynden-Bell, R. M. Lynden-Bell

The wave functions of boson and fermion gases are known even when the particles have harmonic interactions. Here we generalize these results by solving exactly the N–body Schrödinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in three dimensions. For the harmonic case that function is linear in r2. Explicit N–body solutions are given when U(r) = –2Mh–2V(r) = 𝛇r–1 – 𝛇2r–2. Here M is the sum of the masses and r2 = 1/2 M–2ΣmImJ(xI – xJ)2. For general U(r) the solution is given in terms of the one– or two–body problem with potential U(r) in three dimensions. The degeneracies of the levels are derived for distinguishable particles, for bosons of spin zero and for spin 1/2 fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N–body wave function. The N–body forces involved in these extraordinary N–body problems are not the usual sums of two–body interactions, but nor are forces between quarks or molecules. Bose–Einstein condensation of particles in three dimensions interacting via these strange potentials can be treated by this method.

arXiv:cond-mat/9904019•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Sep 8, 1999•11 citations

Quantum distribution functions in systems with an arbitrary number of particles

Yu. M. Poluéktov, A. A. Soroka

Expressions for the entropy and equations for the quantum distribution functions in systems of non-interacting fermions and bosons with an arbitrary, including small, number of particles are obtained in the paper

arXiv:2311.03003•Nov 6, 2023•2 citations

Bosons and Fermions

William J. Mullin

Bosons have symmetric wave function under particle exchange, while fermions have antisymmetric wave functions. This leads to differences in behavior of the two kinds of particles even in the gaseous state. Strong repulsive forces between atoms at close range are due to the Pauli principle that forbids two electrons to be in the same energy or position state. A repulsive Pauli pressure operates similarly in white dwarf stars. Bosons undergo Bose–Einstein condensation because of Bose statistics. The wave function symmetry of particles with spin can affect the magnetic states and the behavior of transport properties, for example, viscosity and thermal conductivity. The symmetry properties of bosons at a beam splitter are demonstrated in the Hong–Ou–Mandel effect or in a Michelson interferometer via the Hanbury Brown-Twiss effect. Researchers see boson bunching and fermion antibunching in experiments considered.

Oxford University Press eBooks•Mar 16, 2017•0 citations

Possible Origin of Magnetic Fields in Very Dense Stars

A. P rez Mart nez, Hugo Pérez Rojas, Herman J. Mosquera Cuesta

We discuss the bosonization of a relativistic very dense Fermi gas in a magnetic field and the consequent Bose–Einstein condensation of the resulting relativistic vector gas of charged particles. The model may be applied to paired spin-up electrons. We show that such systems may maintain self-consistently magnetic fields of order 10 10 −10 13 G. That pairing could be the origin of large magnetic fields in some white dwarfs and neutron stars. For fields large enough (~10 13 for white dwarfs), the system becomes unstable and collapses.

Chinese Physics Letters•Oct 27, 2004•8 citations
The wave functions of boson and fermion gases are known even when the particles have harmonic interactions. Here we generalize these results by solving exactly the N–body Schrödinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in three dimensions. For the harmonic case that function is linear in r2. Explicit N–body solutions are given when U(r) = –2Mh–2V(r) = 𝛇r–1 – 𝛇2r–2. Here M is the sum of the masses and r2 = 1/2 M–2ΣmImJ(xI – xJ)2. For general U(r) the solution is given in terms of the one– or two–body problem with potential U(r) in three dimensions. The degeneracies of the levels are derived for distinguishable particles, for bosons of spin zero and for spin 1/2 fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N–body wave function. The N–body forces involved in these extraordinary N–body problems are not the usual sums of two–body interactions, but nor are forces between quarks or molecules. Bose–Einstein condensation of particles in three dimensions interacting via these strange potentials can be treated by this method.
Bosons have symmetric wave function under particle exchange, while fermions have antisymmetric wave functions. This leads to differences in behavior of the two kinds of particles even in the gaseous state. Strong repulsive forces between atoms at close range are due to the Pauli principle that forbids two electrons to be in the same energy or position state. A repulsive Pauli pressure operates similarly in white dwarf stars. Bosons undergo Bose–Einstein condensation because of Bose statistics. The wave function symmetry of particles with spin can affect the magnetic states and the behavior of transport properties, for example, viscosity and thermal conductivity. The symmetry properties of bosons at a beam splitter are demonstrated in the Hong–Ou–Mandel effect or in a Michelson interferometer via the Hanbury Brown-Twiss effect. Researchers see boson bunching and fermion antibunching in experiments considered.
We discuss the bosonization of a relativistic very dense Fermi gas in a magnetic field and the consequent Bose–Einstein condensation of the resulting relativistic vector gas of charged particles. The model may be applied to paired spin-up electrons. We show that such systems may maintain self-consistently magnetic fields of order 10 10 −10 13 G. That pairing could be the origin of large magnetic fields in some white dwarfs and neutron stars. For fields large enough (~10 13 for white dwarfs), the system becomes unstable and collapses.