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

Ukrainian Journal of Physics

Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters

O. M. Chubai, Andrij A. Rovenchak

Published Jun 9, 2020• 5 citations
Publisher

Abstract

Two approaches to the construction of thermodynamics in the framework of the q- and м-formalisms, which correspond to certain deformations of the algebra of the creation–annihilation operators, have been considered. By comparing the obtained results, an approximate, independent of the space dimension, correspondence was revealed between the second virial coefficients for the ideal q- and м-deformed Bose gases. The corresponding discrepancy arises only at the level of the third virial coefficient. A method for emulating the м-deformed Bose gas up to the third virial coefficient inclusive by means of the two-parametric nonadditive Polychronakos statistics is demonstrated.

DOI
10.15407/ujpe65.6.500

Related papers

Deformed gas of p, q-bosons: virial expansion and virial coefficients

Alexandre M. Gavrilik, A. P. Rebesh

In the study of many-particle systems both the interaction of particles can be essential and such feature as their internal (composite) structure. To describe these aspects, the theory of deformed oscillators is very efficient. Viewing the particles as p,q-deformed bosons, in the corresponding p,q-Bose gas model we obtain in explicit form virial expansion along with the 2nd to 5th virial coefficients. The obtained virial coefficients depend on the deformation parameters p,q in the form symmetric under p<->q, and at p->1, q->1 turn into those known for usual bosons. Besides real parameters, we analyze the case of complex mutually conjugate p and q and find interesting implications. Also, the critical temperature is derived (for the p,q-Bose gas) and compared with the T_c of standard case of Bose condensation. Similar results are presented for the deformed Bose gas model of the Tamm-Dancoff type.

•Aug 14, 2016•36 citations

DEFORMED GAS OF p, q-BOSONS: VIRIAL EXPANSION AND VIRIAL COEFFICIENTS

A. M. GAVRILIK, A. P. REBESH

In the study of many-particle systems both the interaction of particles can be essential and such feature as their internal (composite) structure. To describe these aspects, the theory of deformed oscillators is very efficient. Viewing the particles as p, q-deformed bosons, in the corresponding p, q-Bose gas model we obtain in explicit form virial expansion along with the 2nd to 5th virial coefficients. The obtained virial coefficients depend on the deformation parameters p, q in the form symmetric under p ↔ q, and at p → 1, q → 1 turn into those known for usual bosons. Besides real parameters, we analyze the case of complex mutually conjugate p and q and find interesting implications. Also, the critical temperature is derived (for the p, q-Bose gas) and compared with the Tc of standard case of bosons condensation. Similar results are presented for the deformed Bose gas model of the Tamm–Dancoff (TD) type.

arXiv:1111.7216•Modern Physics Letters B•Feb 3, 2012•43 citations

An interacting ensemble of particles in the context of quantum algebra

Antonio Maria Scarfone, P. Narayana Swamy

In the framework of the q -deformed oscillator algebra we investigate the nature of the interaction among the particles of a free q -boson gas with a view to interpreting the interaction in terms of the general properties of the q -deformation. It is shown that many thermodynamic quantities characterizing the q -boson system can be expressed as power series in the number of particles operator or as a series in the deformation parameter q , implying that the q -deformation can originate from the interaction among the particles of the ensemble. As an example, we derive the virial expansion of the q -boson gas, showing that the lowest order coefficient reduces to the standard virial coefficient of an undeformed boson gas, while the higher order coefficients contain effects arising from interaction.

Journal of Statistical Mechanics Theory and Experiment•Feb 23, 2009•23 citations

An interacting particles system revisited in the framework of theq-deformed algebra

Antonio Maria Scarfone, P Narayana Swamy

We discuss the possibility of interpreting a q-deformed non-interacting system as incorporating the effects of interactions among its particles. This can be accomplished, for instance, in an ensemble of $q$-Bosons by means of the virial expansion of a real gas in powers of the deformed parameter. The lowest order virial coefficient reduces to the case of the standard, non-interacting Bose gas, while the higher order virial coefficients contain effects arising from the interaction. The same picture can be drawn in a quantum mechanical system where it is shown that the q-deformed momentum can be expanded in a series contains high-order powers of the standard quantum phase-space variables. Motivated by this result, we introduce, in the classical framework, a transformation relating the momentum of a free system with the momentum of an interacting system. It is shown that the canonical quantization applied to the interacting system imply a q-deformed quantization for the free system.

arXiv:0807.2510•Journal of Physics A Mathematical and Theoretical•Jun 16, 2008•30 citations

Deformed quantum statistics in two dimensions

A. Lavagno, Narayana Swamy, P.

It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two-dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particles, are no longer identical.

•Jan 1, 2009•10 citations

The quon field from the thermal field theory: Algebra, condensation and anyonic behavior

W. S. Chung, Abdullah Algin

A q-deformed field theory at finite temperature is presented and its related thermo field dynamics is constructed. This enables us to introduce the quon field, whose Lagrangian leads to a q-deformed partition function. Accordingly, the general thermostatistical properties of a gas model of quon fields, such as the q-deformed statistical distribution function describing an intermediate-statistics behavior and the equation of state in two and three dimensions, are investigated. For low temperatures, the conditions under which Bose–Einstein-like condensation would occur in the quon gas model are discussed. It is shown that the critical temperature of such a gas is higher than that of the usual Bose gas for values of the model parameter q in the range [Formula: see text]. For high temperatures, possible anyonic behavior of the present quon gas model in two spatial dimensions is studied through an analysis of the effect of deformation on the second and third virial coefficients in the equation of state. The results obtained in this work reveal the ability of the model for analyzing a parastatistical behavior of systems with quasiparticles and put forward it as a possible candidate for effectively modeling the properties of some exotic quantum states, such as in the case of dark matter constituents.

Modern Physics Letters A•Jan 31, 2026•0 citations
Two approaches to the construction of thermodynamics in the framework of the q- and м-formalisms, which correspond to certain deformations of the algebra of the creation–annihilation operators, have been considered. By comparing the obtained results, an approximate, independent of the space dimension, correspondence was revealed between the second virial coefficients for the ideal q- and м-deformed Bose gases. The corresponding discrepancy arises only at the level of the third virial coefficient. A method for emulating the м-deformed Bose gas up to the third virial coefficient inclusive by means of the two-parametric nonadditive Polychronakos statistics is demonstrated.
In the study of many-particle systems both the interaction of particles can be essential and such feature as their internal (composite) structure. To describe these aspects, the theory of deformed oscillators is very efficient. Viewing the particles as p,q-deformed bosons, in the corresponding p,q-Bose gas model we obtain in explicit form virial expansion along with the 2nd to 5th virial coefficients. The obtained virial coefficients depend on the deformation parameters p,q in the form symmetric under p<->q, and at p->1, q->1 turn into those known for usual bosons. Besides real parameters, we analyze the case of complex mutually conjugate p and q and find interesting implications. Also, the critical temperature is derived (for the p,q-Bose gas) and compared with the T_c of standard case of Bose condensation. Similar results are presented for the deformed Bose gas model of the Tamm-Dancoff type.
In the study of many-particle systems both the interaction of particles can be essential and such feature as their internal (composite) structure. To describe these aspects, the theory of deformed oscillators is very efficient. Viewing the particles as p, q-deformed bosons, in the corresponding p, q-Bose gas model we obtain in explicit form virial expansion along with the 2nd to 5th virial coefficients. The obtained virial coefficients depend on the deformation parameters p, q in the form symmetric under p ↔ q, and at p → 1, q → 1 turn into those known for usual bosons. Besides real parameters, we analyze the case of complex mutually conjugate p and q and find interesting implications. Also, the critical temperature is derived (for the p, q-Bose gas) and compared with the Tc of standard case of bosons condensation. Similar results are presented for the deformed Bose gas model of the Tamm–Dancoff (TD) type.
In the framework of the q -deformed oscillator algebra we investigate the nature of the interaction among the particles of a free q -boson gas with a view to interpreting the interaction in terms of the general properties of the q -deformation. It is shown that many thermodynamic quantities characterizing the q -boson system can be expressed as power series in the number of particles operator or as a series in the deformation parameter q , implying that the q -deformation can originate from the interaction among the particles of the ensemble. As an example, we derive the virial expansion of the q -boson gas, showing that the lowest order coefficient reduces to the standard virial coefficient of an undeformed boson gas, while the higher order coefficients contain effects arising from interaction.
We discuss the possibility of interpreting a q-deformed non-interacting system as incorporating the effects of interactions among its particles. This can be accomplished, for instance, in an ensemble of qqq-Bosons by means of the virial expansion of a real gas in powers of the deformed parameter. The lowest order virial coefficient reduces to the case of the standard, non-interacting Bose gas, while the higher order virial coefficients contain effects arising from the interaction. The same picture can be drawn in a quantum mechanical system where it is shown that the q-deformed momentum can be expanded in a series contains high-order powers of the standard quantum phase-space variables. Motivated by this result, we introduce, in the classical framework, a transformation relating the momentum of a free system with the momentum of an interacting system. It is shown that the canonical quantization applied to the interacting system imply a q-deformed quantization for the free system.
It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two-dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particles, are no longer identical.
A q-deformed field theory at finite temperature is presented and its related thermo field dynamics is constructed. This enables us to introduce the quon field, whose Lagrangian leads to a q-deformed partition function. Accordingly, the general thermostatistical properties of a gas model of quon fields, such as the q-deformed statistical distribution function describing an intermediate-statistics behavior and the equation of state in two and three dimensions, are investigated. For low temperatures, the conditions under which Bose–Einstein-like condensation would occur in the quon gas model are discussed. It is shown that the critical temperature of such a gas is higher than that of the usual Bose gas for values of the model parameter q in the range [Formula: see text]. For high temperatures, possible anyonic behavior of the present quon gas model in two spatial dimensions is studied through an analysis of the effect of deformation on the second and third virial coefficients in the equation of state. The results obtained in this work reveal the ability of the model for analyzing a parastatistical behavior of systems with quasiparticles and put forward it as a possible candidate for effectively modeling the properties of some exotic quantum states, such as in the case of dark matter constituents.