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

Modern Physics Letters B

NEW INCARNATIONS OF INFINITE STATISTICS

Prasanta Kumar Panigrahi, S. Chaturvedi, Venkatraman Srinivasan

Published Mar 10, 1995• 1 citation
Publisher

Abstract

In this paper, we present two new realizations of infinite statistics and construct their respective number operators in a simple manner. One of the realizations assumes the individual oscillators to be bosonic but the mutually commutation relationship (CR) to be of the quonic form. Interestingly, the system of mutually commuting oscillators satisfying individual relations of the type [Formula: see text] (no sum over i) is shown to describe a collection of bosons. This demonstrates that for these examples the mutual CRs between the oscillators decide the statistics.

DOI
10.1142/s0217984995000358

Related papers

Multi—mode q—oscillator algebras with q^2（k＋1）=1 and related thermo field dynamics

高亚军

A type of multi-mode q-oscillator algebra with q^2(k+1)=1 is set up and the associated qk-thermo field dynamics is constructed for all k=1,2,…，∞ in a unified form.It is demonstrated that these qk-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics(axiomatized form for statistical physics).This means that we obtain infinitely many realizations of the algebraic scheme,which extend the consideration of Ojima [1981 Ann.Phys.137 1] and contain the usual thermo field dynamics for the fermionic (k=1) and bosonic (k=∞) systems as special cases.As simple applications,the qk-statistical average of some operators are given.

中国物理B：英文版•Jun 12, 2005•0 citations

Multi-mode q-oscillator algebras with q2(k + 1) = 1 and related thermo field dynamics

Ya-Jun Gao

A type of multi-mode q-oscillator algebra with q2(k + 1) = 1 is set up and the associated qk-thermo field dynamics is constructed for all k = 1,2,,∞ in a unified form. It is demonstrated that these qk-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics (axiomatized form for statistical physics). This means that we obtain infinitely many realizations of the algebraic scheme, which extend the consideration of Ojima [1981 Ann. Phys. 137 1] and contain the usual thermo field dynamics for the fermionic (k = 1) and bosonic (k = ∞) systems as special cases. As simple applications, the qk-statistical average of some operators are given.

Chinese Physics•May 14, 2002•1 citation

Quons, an interpolation between bose and fermi oscillators

Oscar Wallace Greenberg

After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics and infinite statistics, I discuss the statistics of ``quons'' (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the $q$-deformed commutation relation (the quon algebra or q-mutator) which interpolates between fermions and bosons. I emphasize that the operator for interaction with an external source must be an effective Bose operator in all cases. To accomplish this for parabose, parafermi and quon operators, I introduce parabose, parafermi and quon Grassmann numbers, respectively. I also discuss interactions of non-relativistic quons, quantization of quon fields with antiparticles, calculation of vacuum matrix elements of relativistic quon fields, demonstration of the TCP theorem, cluster decomposition, and Wick's theorem for relativistic quon fields, and the failure of local commutativity of observables for relativistic quon fields. I conclude with the bound on the parameter $q$ for electrons due to the Ramberg-Snow experiment.

arXiv:cond-mat/9301002•Jan 5, 1993•7 citations

QUANTUM BOLTZMANN STATISTICS IN INTERACTING SYSTEMS

Luigi Accardi, Sergei Vladimirovich Kozyrev

Collective operators for generic quantum systems with discrete spectrum are investigated. These operators, considered as operators in the entagled Fock space (space generated by action of collective creations of the vacuum) satisfy a particular kind of quantum Boltzmann (or free) commutational relations.

Quantum Probability and Infinite Dimensional Analysis•Jan 1, 2003•0 citations

Statistics with number operator C C*

Steven Robbins

The number operator a*a, where a is an annihilation operator, plays a fundamental role in the statistics of bosons and fermions. However, it is possible for other statistics to have the same number operator. We have previously shown that for one degree of freedom there is a type of statistics having this number operator corresponding to each p which is a positive integer or ∞. Fermions are obtained when p = 1 and bosons are obtained when p = ∞. No state can have more than p particles. In order to treat many degrees of freedom it is necessary to first consider the case of one degree of freedom differently. We show here that for more degrees of freedom a similar situation occurs but for each case other than bosons and fermions there is a positive integer q, such that no state can have more than q particles, even when the number of degrees of freedom is infinite. Thus these statistics are probably not physically realizable except in an approximate way.

Journal of Mathematical Physics•Jan 1, 1982•1 citation

Statistics of q-oscillators, quons and relations to fractional statistics

Масуд Чайчиан, R. González Felipe, Claus Montonen

The statistics of q-oscillators, quons, and, to some extent, of anyons are studied and the basic differences among these objects are pointed out In particular, the statistical distributions for different bosonic and fermionic q-oscillators are found for their corresponding Fock space representations in the case when the Hamiltonian is identified with the number operator. In this case and for non-relativistic particles, the single-particle temperature Green function is defined with q-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic q-gases in an arbitrary space dimension are found near Bose statistics, as well as that for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated.

arXiv:hep-th/9304111•Journal of Physics A Mathematical and General•Aug 21, 1993•159 citations
In this paper, we present two new realizations of infinite statistics and construct their respective number operators in a simple manner. One of the realizations assumes the individual oscillators to be bosonic but the mutually commutation relationship (CR) to be of the quonic form. Interestingly, the system of mutually commuting oscillators satisfying individual relations of the type [Formula: see text] (no sum over i) is shown to describe a collection of bosons. This demonstrates that for these examples the mutual CRs between the oscillators decide the statistics.
A type of multi-mode q-oscillator algebra with q^2(k+1)=1 is set up and the associated qk-thermo field dynamics is constructed for all k=1,2,…，∞ in a unified form.It is demonstrated that these qk-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics(axiomatized form for statistical physics).This means that we obtain infinitely many realizations of the algebraic scheme,which extend the consideration of Ojima [1981 Ann.Phys.137 1] and contain the usual thermo field dynamics for the fermionic (k=1) and bosonic (k=∞) systems as special cases.As simple applications,the qk-statistical average of some operators are given.
A type of multi-mode q-oscillator algebra with q2(k + 1) = 1 is set up and the associated qk-thermo field dynamics is constructed for all k = 1,2,,∞ in a unified form. It is demonstrated that these qk-thermo field dynamics can all be nicely fitted into the algebraic formulation of statistical mechanics (axiomatized form for statistical physics). This means that we obtain infinitely many realizations of the algebraic scheme, which extend the consideration of Ojima [1981 Ann. Phys. 137 1] and contain the usual thermo field dynamics for the fermionic (k = 1) and bosonic (k = ∞) systems as special cases. As simple applications, the qk-statistical average of some operators are given.
After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics and infinite statistics, I discuss the statistics of ``quons'' (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the qqq-deformed commutation relation (the quon algebra or q-mutator) which interpolates between fermions and bosons. I emphasize that the operator for interaction with an external source must be an effective Bose operator in all cases. To accomplish this for parabose, parafermi and quon operators, I introduce parabose, parafermi and quon Grassmann numbers, respectively. I also discuss interactions of non-relativistic quons, quantization of quon fields with antiparticles, calculation of vacuum matrix elements of relativistic quon fields, demonstration of the TCP theorem, cluster decomposition, and Wick's theorem for relativistic quon fields, and the failure of local commutativity of observables for relativistic quon fields. I conclude with the bound on the parameter qqq for electrons due to the Ramberg-Snow experiment.
The number operator a*a, where a is an annihilation operator, plays a fundamental role in the statistics of bosons and fermions. However, it is possible for other statistics to have the same number operator. We have previously shown that for one degree of freedom there is a type of statistics having this number operator corresponding to each p which is a positive integer or ∞. Fermions are obtained when p = 1 and bosons are obtained when p = ∞. No state can have more than p particles. In order to treat many degrees of freedom it is necessary to first consider the case of one degree of freedom differently. We show here that for more degrees of freedom a similar situation occurs but for each case other than bosons and fermions there is a positive integer q, such that no state can have more than q particles, even when the number of degrees of freedom is infinite. Thus these statistics are probably not physically realizable except in an approximate way.
The statistics of q-oscillators, quons, and, to some extent, of anyons are studied and the basic differences among these objects are pointed out In particular, the statistical distributions for different bosonic and fermionic q-oscillators are found for their corresponding Fock space representations in the case when the Hamiltonian is identified with the number operator. In this case and for non-relativistic particles, the single-particle temperature Green function is defined with q-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic q-gases in an arbitrary space dimension are found near Bose statistics, as well as that for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated.