DISTRIBUTION OF PARASTATISTICS FUNCTIONS: AN OVERVIEW OF THERMODYNAMICS PROPERTIES

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R. Yosi Aprian Sari

2016-05-01

Full Text Available This study aims to determine the thermodynamic properties of the parastatistics system of order two. The thermodynamic properties to be searched include the Grand Canonical Partition Function (GCPF Z, and the average number of particles N. These parastatistics systems is in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD and Bose-Einstein (BE. Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple thermodynamic functions for parastatistics system of order two are derived. The recursion linkages are then used to calculate the thermodynamic functions of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. From these results we concluded that from the Grand Canonical Partition Function (GCPF, Z, the thermodynamics properties of parastatistics system of order two (paraboson and parafermion can be derived and have similar shape with parastatistics system of order one (Boson and Fermion. The similarity of the graph shows similar thermodynamic properties.   Keywords: parastatistics, thermodynamic properties

Quantum field theory and parastatistics

International Nuclear Information System (INIS)

Ohnuki, Y.; Kamefuchi, S.

1982-01-01

This book is an introduction to the second quantization of the wave functions of particles obeying the parastatistics. After a general introduction to the canonical quantization for the case of paracommutation relations the nonrelativistic field theory is considered. Thereafter the extension to the relativistic range is discussed. Finally some special problems in connection with parafields are considered. (HSI)

Toward a Parastatistics in Quantum Nonextensive Statistical Mechanics

Science.gov (United States)

Zaripov, R. G.

2018-05-01

On the basis of Bose quantum states in parastatistics the equations for the equilibrium distribution of quantum additive and nonextensive systems are determined. The fluctuations and variances of physical quantities for the equilibrium system are found. The Abelian group of microscopic entropies is determined for the composition law with a quadratic nonlinearity.

D-Dimensional ideal gas in parastatistics.: thermodynamic properties

International Nuclear Information System (INIS)

Sousa Vieira, M. C. de; Tsallis, C.

1986-01-01

A parastatistics ideal gas with energy spectrum ε is proportional to |k| → sup (α) (α>0) or even more general in a d-dimensional box with volume V (periodic boundary conditions), the number N of the gas particles being well determined (real particles) or not (quasi particles), is considered. The main thermodynamic quantities (chemical potential, internal energy, specific heat C, equation of state, latent heat, average numbers of particles) for arbitrary d,α, T (temperature) and p (maximal number of particles per state allowed in the parastatistics), are calculated. The main asymptotic regimes are worked out explicitly. In particular, the Bose-Einstein condensation for fixed density, N/V appears as a non uniform convergence in the p→ ∞ limit, in complete analogy with the standard critical phenomena which appear in interacting systems in the N →∞ limit. The system behaves essentially like a Fermi-Dirac one for all finite values of p, and reveals a Bose-Einstein behavior only in the p → ∞ limit. For instance, at low temperatures C ∝ T if p d/α if p → ∞. Finally the Sommerfeld integral and its expansion are generalized to an arbitrary finite p. (author) [pt

Hopf structure and Green ansatz of deformed parastatistics algebras

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Aneva, Boyka [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, bld. Tsarigradsko chaussee 72, BG-1784 Sofia (Bulgaria); Popov, Todor [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, bld. Tsarigradsko chaussee 72, BG-1784 Sofia (Bulgaria)

2005-07-22

Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed Bose and Fermi representations. The construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized Green ansatz.

Some studies in parastatistical theories and its applications in the internal symmetry of elementary particles

International Nuclear Information System (INIS)

Silva, H.V. da.

1984-01-01

The results of investigations in parastatistical theories and in their applications to the internal symmetries of elementary particles are present. The paraquantization and the 'generalized paraquantization' (of Levine and Tomozawa) of the relativistic Schroedinger wave equations for non-zero mass and arbitrary spin (s), involving locally covariant wave functions, Ψ o,s + Ψ s,o are executed, and the restrictions resulting from the criterion of microscopic causality and the manner of establishment of the connection between spin and statistics in these quantizations are explicitly demonstrated. (Author) [pt

A q-deformation of the parastatistics and an alternative to the Chevalley description of Uq[osp(2n+1/2m)

International Nuclear Information System (INIS)

Palev, T.D.

1997-08-01

The paper contains essentially two new results. Physically, a deformation of the parastatistics in a sense of quantum groups is carried out. Mathematically, an alternative to the Chevalley description of the quantum orthosymplectic superalgebra U q [osp(2n + 1/2m)] in terms of m pairs of deformed parabosons and n pairs of deformed parafermions is outlined. (author). 35 refs

Entanglement for multipartite systems of indistinguishable particles

Energy Technology Data Exchange (ETDEWEB)

Grabowski, Janusz [Polish Academy of Sciences, Institute of Mathematics, Sniadeckich 8, PO Box 21, 00-956 Warsaw (Poland); Kus, Marek [Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02-668 Warszawa (Poland); Marmo, Giuseppe, E-mail: jagrab@impan.pl, E-mail: marek.kus@cft.edu.pl, E-mail: marmo@na.infn.it [Dipartimento di Scienze Fisiche, Universita ' Federico II' di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte Sant Angelo, Via Cintia, I-80126 Napoli (Italy)

2011-04-29

We analyze the concept of entanglement for a multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics. We use the representation theory of symmetry groups to formulate a unified approach to this problem in terms of simple tensors with an appropriate symmetry. For an arbitrary parastatistics, we define the S-rank generalizing the notion of the Schmidt rank. The S-rank, defined for all types of tensors, serves for distinguishing entanglement of pure states. In addition, for Bose and Fermi statistics, we construct an analog of the Jamiolkowski isomorphism.

Hopf Structures on Standard Young Tableaux

International Nuclear Information System (INIS)

Loday, Jean-Louis; Popov, Todor

2010-01-01

We review the Poirier-Reutenauer Hopf structure on Standard Young Tableaux and show that it is a distinguished member of a family of Hopf structures. The family in question is related to deformed parastatistics.

Parastatistics and gauge symmetries

International Nuclear Information System (INIS)

Govorkov, A.B.

1982-01-01

A possible formulation of gauge symmetries in the Green parafield theory is analysed and the SO(3) gauge symmetry is shown to be on a distinct status. The Greenberg paraquark hypothesis turns out to be not equivalent to the hypothesis of quark colour SU(3)sub(c) symmetry. Specific features of the gauge SO(3) symmetry are discussed, and a possible scheme where it is an exact subgroup of the broken SU(3)sub(c) symmetry is proposed. The direct formulation of the gauge principle for the parafield represented by quaternions is also discussed

Algebraic structure of the Green's ansatz and its q-deformed analogue

International Nuclear Information System (INIS)

Palev, T.D.

1994-08-01

The algebraic structure of the Green's ansatz is analyzed in such a way that its generalization to the case of q-deformed para-Bose and para-Fermi operators is becoming evident. To this end the underlying Lie (super) algebraic properties of the parastatistics are essentially used. (author). 41 refs

Boltzmann, Gibbs and Darwin-Fowler approaches in parastatistics

International Nuclear Information System (INIS)

Ponczek, R.L.; Yan, C.C.

1976-01-01

Derivations of the equilibrium values of occupation numbers are made using three approaches, namely, the Boltzmann 'elementary' one, the ensemble method of Gibbs, and that of Darwin and Fowler as well [pt

The spinorial character of the gentilionic baryon states

International Nuclear Information System (INIS)

Cattani, M.S.D.; Fernandes, N.C.

1986-06-01

It is shown that the wavefunction, in an internal colour space of three quarks taken as gentileons, has a bi-spinorial character. In this context, the formalism differs drastically from parastatistics and fermionic theories of quarks. As a direct consequence of the spinorial character the SU(3) colour representation can naturally be incorporated into the S 3 gentilionic symmetry and a selection rule for quark confinement is deduced. Comparing the results with Dirac's bi-spinorial formulation and with Prentki-d'Espagnat theory, striking resemblances are found. (Author) [pt

Generalized field quantization and statistics of elementary particles

International Nuclear Information System (INIS)

Govorkov, A.V.

1994-01-01

Generalized schemes for the quantization of free fields based on the deformed trilinear relations of Green are investigated. A theorem shows that in reality continuous deformation is impossible. In particular, it is shown that a open-quotes smallclose quotes violation of the ordinary Fermi and Bose statistics is impossible both in the framework of local field theory, corresponding to parastatistics of finite orders, and in the framework of nonlocal field theory, corresponding to infinite statistics. The existence of antiparticles plays a decisive role in establishing the matter case. 23 refs

Algebraic QFT as a framework for classification and model-building. A heretic view of the new kinematics

International Nuclear Information System (INIS)

Schroer, B.

1990-01-01

We show that the algebraic structure encountered first in conformal QFT 2 corresponds to the multiciplicity-free parastatistics description of H. Green of 1953. We give arguments in favour of the dictum that QFT, in contradistinction to Quantum Mechanics, does not have to rely on quantization but rather allows for a formulation and classification in terms of intrinsic quantum principles. We interpret the Karowski-Weisz-Smirnov form-factor program in this light and comment on some properties of anyons and plektons which may be relevant for condensed matter physics (the enigma of Non-Fermi-Liquid-States)

Graded Fock-like representations for a system of algebraically interacting paraparticles

International Nuclear Information System (INIS)

Kanakoglou, Konstantinos; Herrera-Aguilar, Alfredo

2011-01-01

We will present and study an algebra describing a mixed paraparticle model, known in the bibliography as 'The Relative Parabose Set (RPBS)'. Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom P (1,1) BF , we will construct a class of Fock-like representations of this algebra, dependent on a positive parameter p a kind of generalized parastatistics order. Mathematical properties of the Fock-like modules will be investigated for all values of p and constructions such as ladder operators, irreducibility (for the carrier spaces) and (Z 2 x Z 2 )-gradings (for both the carrier spaces and the algebra itself) will be established.

Parastatistics and the equation of state for the early universe

International Nuclear Information System (INIS)

Aldrovandi, R.; Monte Lima, I. do.

1982-01-01

The equation of state for an ideal mixture of relativistic quantum gases obeying any (para-) statistics is given. Recursion formulas are obtained for the distribution functions and correlations are analysed. The equation of state can be applied to the early Universe, allowing the quarks to be treated either as coloured fermions of (unequivalently) as parafermions of order 3. In the latter case, a tendency to aggregate into triads by a mere statistical effect is exhibited. (Author) [pt

On parasupersymmetries and relativistic descriptions for spin one particles. Pt. 1. The free context

International Nuclear Information System (INIS)

Beckers, J.; Debergh, N.; Nikitin, A.G.

1995-01-01

This series of two papers is devoted to a constructive review of the relativistic wave equations for vector mesons due to the recent impact of spin one developments in connection with parasupersymmetric quantum mechanics. The free case as well as the interacting context with an electromagnetic field will be successively visited and discussed. Their associated parasupersymmetric properties will be pointed out. In this first part, the free context is presented by studying systematically the (symmetric) forms of wave equations subtended by a 16-dimensional reducible representation of the Lie algebra sl (2, C) or, evidently, so (3, 1), this representation playing a well known role in p = 2-parastatistical developments. Their hamiltonian forms are also discussed and some second order descriptions are finally reviewed. (orig.)

Current algebra for parafields

International Nuclear Information System (INIS)

Palev, Ch.D.

1976-01-01

Within the framework of the Lagrangean QFT a generalization of canonical commutation and anticommutation relations in terms of three-linear commutation relations, corresponding to the parastatistics, s discussed. A detailed derivation of these three-linear relations for a set of parafermi fields is presented. Then for a Lagrangean, depending of a family of parabose fields and a family of paraferm fields, is shown that the fundamental hypothesis of current algebra is valid. In other words, the currents corresponding to the linear gauge transformations are found to meet the commutation relation: [Jsub(f)sup(0)(x), Jsub(g)sup(0)]sub(x 0 =y 0 ) = -idelta(x vector - y vector)Jsub([f,g])sup(0) (x), where Jsub(f)sup(0) is a time component of the current, corresponding to transformation f. (S.P.)

The Pauli exclusion principle origin, verifications and applications

CERN Document Server

Kaplan, Ilya G

2017-01-01

This is the first scientific book devoted to the Pauli Exclusion Principle, which is a fundamental principle of quantum mechanics and is permanently applied in chemistry, physics, molecular biology and in physical astronomy. However, while the principle has been studied for more than 90 years, rigorous theoretical foundations still have not been established and many unsolved problems remain. Following an introduction and historical survey, this book discusses the still unresolved questions around this fundamental principle. For instance, why, according to the Pauli Exclusion Principle, are only symmetric and antisymmetric permutation symmetries for identical particles realized, while the Schrödinger equation is satisfied by functions with any permutation symmetry? Chapter 3 covers possible answers to this, while chapter 4 presents effective and elegant methods for finding the Pauli-allowed states in atomic, molecular and nuclear spectroscopy. Chapter 5 discusses parastatistics and fractional statistics, dem...