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

Russian Physics Journal

Statistical physics as an approximate method in quantum mechanics of many particle systems in the occupation number representation

A. N. Kushnirenko

Published Oct 1, 1989• 0 citations
Publisher
DOI
10.1007/bf00898323

Related papers

One method to derive the form of general operators in occupation particle number representation

Ren Zheng-xu

The expansion of single- particle transition operator( defined as the product of creation and annihilation operator,namely a+iajin single- particle state is obtained through the form of single- operator in occupation particle number representation,and the commutation relations for transition operator and creation( annihilation) operator are also given,then based on these conclusions,the form of general two- and n- particle operators in occupation particle number representation can be derived succinctly without distinguishing the statistical property of identical particle system.

College Physics•Jan 1, 2015•0 citations

Quantum mechanics as an approximation of statistical mechanics for classical fields

Andrei Yu. Khrennikov

Reports on Mathematical Physics•Dec 1, 2007•6 citations

Quantum Mechanics of a Many-Boson System and the Representation of Canonical Variables

Hiroshi Ezawa

We present a method of treating the assembly of interacting bosons under Bose-Einstein condensation. Without applying the Bogoliubov approximation in which the creation and the annihilation operators of zero-momentum particles are replaced by a c number, we keep the quantum nature of these operators—thus the title, ``Quantum Mechanics.'' The method is a quantum mechanical adaptation of the theory of small oscillation. The oscillation means the fluctuation of the number of condensed particles. The interaction between particles determines the stability of this oscillation. When it is stable and its amplitude is not macroscopic, the Bogoliubov approximation is valid. In this way, our method provides a validity criterion for the Bogoliubov approximation as well as an estimation of the errors thereby committed. We have to note that the excitations associated with the fluctuation of condensed particles can never be obtained within that approximation. Our method is applied to the Huang model, the assembly of bosons interacting through a hard core plus weak attractive potential. Having found that, within the physically accessible range of the particle density, the above-mentioned oscillation is stable, we can conclude that Huang's treatment is well founded. We have discussed the mathematical background of our approximation by invoking the representation theory of canonical variables of an infinitely large system.

Journal of Mathematical Physics•Mar 1, 1965•28 citations

General approach to quantum mechanics as a statistical theory

Todd Tilma

•Jan 1, 2019•0 citations

Summary of Quantum and Statistical Mechanics

Michele Cini, Francesco Fucito, Mauro Sbragaglia

Unitext•Jan 1, 2012•0 citations

Quantum Statistical Mechanics for Systems of Identical Part

Fabien Paillusson

This chapter follows on from the previous chapter in quantum statistical mechanics but specialising on systems with identical particles. Using Gibbs prescritpion on generic states from Chapter 3, the occupation number representation is introduced. Constraints imposed on statistics by irreducible representations of the permutation group are discussed. These group-theoretic considerations are used to justify the use of Gentile’s parastatistics. Fermions and bosons are introduced as special cases of Gentile’s statistics, corresponding to the trivial representation of the permutation group for bosons, and the sign representation of the permutation group for fermions. Basic applications to fermions and bosons is given, including the Fermi–Dirac and Bose–Einstein statistics. A detailed expose of why photons are said to have zero chemical potential is also proposed.

Cambridge University Press eBooks•Jul 28, 2025•0 citations
The expansion of single- particle transition operator( defined as the product of creation and annihilation operator,namely a+iajin single- particle state is obtained through the form of single- operator in occupation particle number representation,and the commutation relations for transition operator and creation( annihilation) operator are also given,then based on these conclusions,the form of general two- and n- particle operators in occupation particle number representation can be derived succinctly without distinguishing the statistical property of identical particle system.
We present a method of treating the assembly of interacting bosons under Bose-Einstein condensation. Without applying the Bogoliubov approximation in which the creation and the annihilation operators of zero-momentum particles are replaced by a c number, we keep the quantum nature of these operators—thus the title, ``Quantum Mechanics.'' The method is a quantum mechanical adaptation of the theory of small oscillation. The oscillation means the fluctuation of the number of condensed particles. The interaction between particles determines the stability of this oscillation. When it is stable and its amplitude is not macroscopic, the Bogoliubov approximation is valid. In this way, our method provides a validity criterion for the Bogoliubov approximation as well as an estimation of the errors thereby committed. We have to note that the excitations associated with the fluctuation of condensed particles can never be obtained within that approximation. Our method is applied to the Huang model, the assembly of bosons interacting through a hard core plus weak attractive potential. Having found that, within the physically accessible range of the particle density, the above-mentioned oscillation is stable, we can conclude that Huang's treatment is well founded. We have discussed the mathematical background of our approximation by invoking the representation theory of canonical variables of an infinitely large system.
This chapter follows on from the previous chapter in quantum statistical mechanics but specialising on systems with identical particles. Using Gibbs prescritpion on generic states from Chapter 3, the occupation number representation is introduced. Constraints imposed on statistics by irreducible representations of the permutation group are discussed. These group-theoretic considerations are used to justify the use of Gentile’s parastatistics. Fermions and bosons are introduced as special cases of Gentile’s statistics, corresponding to the trivial representation of the permutation group for bosons, and the sign representation of the permutation group for fermions. Basic applications to fermions and bosons is given, including the Fermi–Dirac and Bose–Einstein statistics. A detailed expose of why photons are said to have zero chemical potential is also proposed.