scholarly journals THERMODYNAMIC PROPERTIES OF A QUANTUM GROUP BOSON GAS GLp,q(2)

2002 ◽  
Vol 17 (12) ◽  
pp. 701-710 ◽  
Author(s):  
AHMED JELLAL
Keyword(s):  
Thermodynamic Properties ◽  
Quantum Group ◽  
Present System ◽  
Bosonic System ◽  
Deformation Parameters ◽  
Number Of Particles

An approach is proposed enabling to effectively describe the behavior of a bosonic system. The approach uses the quantum group GL p,q(2) formalism. Indeed, considering a bosonic Hamiltonian in terms of the GL p,q(2) generators, it is shown that its thermodynamic properties are connected to deformation parameters p and q. For instance, the average number of particles and the pressure have been computed. If p is fixed to be the same value for q, our approach coincides perfectly with some results developed recently in this subject. The ordinary results, of the present system, can be found when we take the limit p = q = 1.

scholarly journals DISTRIBUTION OF PARASTATISTICS FUNCTIONS: AN OVERVIEW OF THERMODYNAMICS PROPERTIES

2016 ◽  
Vol 4 (2) ◽  
pp. 179
Author(s):  
R. Yosi Aprian Sari ◽  
W. S. B. Dwandaru
Keyword(s):  
Partition Function ◽  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Canonical Partition Function ◽  
Thermodynamics Properties ◽  
Grand Canonical Partition Function ◽  
Bose Einstein ◽  
Grand Canonical ◽  
Number Of Particles

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

scholarly journals Quantum E(2) groups for complex deformation parameters

2021 ◽  
pp. 2150021
Author(s):  
Atibur Rahaman ◽  
Sutanu Roy
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Locally Compact ◽  
Complex Deformation ◽  
Circle Group ◽  
Deformation Parameters ◽  
Quantum Analogue ◽  
Group Contraction ◽  
Contraction Procedure ◽  
Matrix Formula

We construct a family of [Formula: see text] deformations of E(2) group for nonzero complex parameters [Formula: see text] as locally compact braided quantum groups over the circle group [Formula: see text] viewed as a quasitriangular quantum group with respect to the unitary [Formula: see text]-matrix [Formula: see text] for all [Formula: see text]. For real [Formula: see text], the deformation coincides with Woronowicz’s [Formula: see text] groups. As an application, we study the braided analogue of the contraction procedure between [Formula: see text] and [Formula: see text] groups in the spirit of Woronowicz’s quantum analogue of the classic Inönü–Wigner group contraction. Consequently, we obtain the bosonization of braided [Formula: see text] groups by contracting [Formula: see text] groups.

scholarly journals Representations and classification of the compact quantum groups Uq(2) for complex deformation parameters

2021 ◽  
pp. 2150020
Author(s):  
Satyajit Guin ◽  
Bipul Saurabh
Keyword(s):  
Quantum Group ◽  
Jacobi Polynomials ◽  
Compact Quantum Group ◽  
Plancherel Formula ◽  
Irreducible Representations ◽  
Complex Deformation ◽  
Deformation Parameters ◽  
Irreducible Components ◽  
The Matrix ◽  
Compact Quantum Groups

In this paper, we obtain a complete list of inequivalent irreducible representations of the compact quantum group [Formula: see text] for nonzero complex deformation parameters [Formula: see text], which are not roots of unity. The matrix coefficients of these representations are described in terms of the little [Formula: see text]-Jacobi polynomials. The Haar state is shown to be faithful and an orthonormal basis of [Formula: see text] is obtained. Thus, we have an explicit description of the Peter–Weyl decomposition of [Formula: see text]. As an application, we discuss the Fourier transform and establish the Plancherel formula. We also describe the decomposition of the tensor product of two irreducible representations into irreducible components. Finally, we classify the compact quantum group [Formula: see text].

scholarly journals THERMODYNAMIC PROPERTIES OF AN INTERACTING HARD-SPHERE BOSE GAS IN A TRAP USING THE STATIC FLUCTUATION APPROXIMATION

2010 ◽  
Vol 24 (24) ◽  
pp. 4779-4809 ◽  
Author(s):  
SALEEM I. QASHOU ◽  
MOHAMED K. AL-SUGHEIR ◽  
ASAAD R. SAKHEL ◽  
HUMAM B. GHASSIB
Keyword(s):  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Occupation Number ◽  
Interaction Strength ◽  
Bose Gas ◽  
Weakly Interacting ◽  
Oscillator Wave Function ◽  
Static Fluctuation Approximation ◽  
Static Fluctuation ◽  
Number Of Particles

A hard-sphere (HS) Bose gas in a trap is investigated at finite temperatures in the weakly interacting regime and its thermodynamic properties are evaluated using the static fluctuation approximation. The energies are calculated with a second-quantized many-body Hamiltonian and a harmonic oscillator wave function. The specific heat capacity, internal energy, pressure, entropy, and the Bose–Einstein occupation number of the system are determined as functions of temperature and for various values of interaction strength and number of particles. It is found that the number of particles plays a more profound role in the determination of the thermodynamic properties of the system than the HS diameter characterizing the interaction, that the critical temperature drops with the increase of the repulsion between the bosons, and that the fluctuations in the energy are much smaller than the energy itself in the weakly interacting regime.

ON A HOPF ALGEBRA RELATED TO THE GLq(2) AND GLp,q(2) QUANTUM GROUPS

1996 ◽  
Vol 11 (04) ◽  
pp. 715-732
Author(s):  
B. BASU-MALLICK
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Quantum Groups ◽  
Nonlinear Realization ◽  
Intimate Connection ◽  
Deformation Parameters ◽  
Two Parameter

By adding one extra generator with the standard GL q(2) quantum group, we construct a Hopf algebra [Formula: see text] which depends on two deformation parameters and five generators. Curiously, it turns out that there exists a nonlinear realization of the two-parameter deformed GL p,q(2) quantum group through generators of this [Formula: see text] algebra. Subsequently, we find the invariant noncommutative planes associated with the [Formula: see text] quantum group and also discuss how the well-known Manin planes corresponding to the GL p,q(2) quantum group can be produced automatically, through such construction. Finally, we consider the “colored” extension of the GL p,q(2) quantum group as well as corresponding noncommutative planes and explore their intimate connection with the “colored” extension of [Formula: see text] Hopf structure.

scholarly journals THERMODYNAMICS OF PSEUDO-HERMITIAN SYSTEMS IN EQUILIBRIUM

2007 ◽  
Vol 22 (15) ◽  
pp. 1075-1084 ◽  
Author(s):  
VÍT JAKUBSKÝ
Keyword(s):  
Thermodynamic Properties ◽  
Physical Interpretation ◽  
Explicit Knowledge ◽  
Positive Definite ◽  
Explicit Calculation ◽  
Constant Number ◽  
Metric Operator ◽  
Number Of Particles

In the study of pseudo(quasi)-hermitian operators, the key role is played by the positive-definite metric operator. It enables physical interpretation of the considered systems. In this paper, we study the pseudo-hermitian systems with constant number of particles in equilibrium. We show that the explicit knowledge of the metric operator is not essential for the study of thermodynamic properties of the system. We introduce a simple example where the physically relevant quantities are derived without explicit calculation of either metric operator or spectrum of the Hamiltonian.

Models of Thermodynamic Properties of Prominences

1979 ◽  
Vol 44 ◽  
pp. 349-355
Author(s):  
R.W. Milkey
Keyword(s):  
Thermodynamic Properties ◽  
Mass Transport ◽  
Emission Spectrum ◽  
Thermodynamic Parameters ◽  
Working Group ◽  
Physical Processes ◽  
Theoretical Concepts ◽  
Group 3 ◽  
Observational Techniques

The focus of discussion in Working Group 3 was on the Thermodynamic Properties as determined spectroscopically, including the observational techniques and the theoretical modeling of physical processes responsible for the emission spectrum. Recent advances in observational techniques and theoretical concepts make this discussion particularly timely. It is wise to remember that the determination of thermodynamic parameters is not an end in itself and that these are interesting chiefly for what they can tell us about the energetics and mass transport in prominences.

Stereo Electron Microscopy Applied to High Resolution Freeze-Etch Replicas

1970 ◽  
Vol 28 ◽  
pp. 306-307
Author(s):  
L. Andrew Staehelin
Keyword(s):  
Electron Microscopy ◽  
Plastic Deformation ◽  
High Resolution ◽  
Smooth Surfaces ◽  
Small Particles ◽  
Membrane Surfaces ◽  
Wide Acceptance ◽  
New Information ◽  
Number Of Particles ◽  
Small Holes

Freeze-etched membranes usually appear as relatively smooth surfaces covered with numerous small particles and a few small holes (Fig. 1). In 1966 Branton (1“) suggested that these surfaces represent split inner mem¬brane faces and not true external membrane surfaces. His theory has now gained wide acceptance partly due to new information obtained from double replicas of freeze-cleaved specimens (2,3) and from freeze-etch experi¬ments with surface labeled membranes (4). While theses studies have fur¬ther substantiated the basic idea of membrane splitting and have shown clearly which membrane faces are complementary to each other, they have left the question open, why the replicated membrane faces usually exhibit con¬siderably fewer holes than particles. According to Branton's theory the number of holes should on the average equal the number of particles. The absence of these holes can be explained in either of two ways: a) it is possible that no holes are formed during the cleaving process e.g. due to plastic deformation (5); b) holes may arise during the cleaving process but remain undetected because of inadequate replication and microscope techniques.

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