Anyonic behavior of quantum group gases

We first introduce and discuss the formalism of $SU_q(N)$-bosons and fermions and consider the simplest Hamiltonian involving these operators. We then calculate the grand partition function for these models and study the high temperature (low density) case of the corresponding gases for $N=2$. We show that quantum group gases exhibit anyonic behavior in $D=2$ and $D=3$ spatial dimensions. In particular, for a $SU_q(2)$ boson gas at $D=2$ the parameter $q$ interpolates within a wider range of attractive and repulsive systems than the anyon statistical parameter.Comment: LaTeX file, 19 pages, two figures ,uses epsf.st

Effect of quantum group invariance on trapped Fermi gases

We study the properties of a thermodynamic system having the symmetry of a quantum group and interacting with a harmonic potential. We calculate the dependence of the chemical potential, heat capacity and spatial distribution of the gas on the quantum group parameter $q$ and the number of spatial dimensions $D$. In addition, we consider a fourth-order interaction in the quantum group fields $\Psi$, and calculate the ground state energy up to first order.Comment: LaTeX file, 20 pages, four figures, uses epsf.sty, packaged as a single tar.gz uuencoded fil

Correlation functions in the factorization approach of nonextensive quantum statistics

We study the long range behavior of a gas whose partition function depends on a parameter q and it has been claimed to be a good approximation to the partition function proposed in the formulation of nonextensive statistical mechanics. We compare our results, at large temperatures and at the critical point, with the case of Boltzmann-Gibbs thermodynamics for the case of a Bose-Einstein gas. In particular, we find that for all temperatures the long range correlations in a Bose gas decrease when the value of q departs from the standard value q=1.Comment: revtex file, 10 pages, two eps style figures, packaged as a single tar.gz fil

Thermodynamic Properties of a Quantum Group Boson Gas GLp,q(2)GL_{p,q}(2)

An approach is proposed enabling to effectively describe the behaviour of a bosonic system. The approach uses the quantum group $GL_{p,q}(2)$ formalism. In effect, 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 $p=q=1$.Comment: 13 pages, Late

q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials

We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator. This allows to construct q-deformed Schroedinger equations in higher dimensions. The equivalence of these Schroedinger equations with those defined on q-Euclidean space in quantum variables is shown. We also define the m-dimensional q-Clifford-Hermite polynomials and show their connection with the q-Laguerre polynomials. These polynomials are orthogonal with respect to an m-dimensional q-integration, which is related to integration on q-Euclidean space. The q-Laguerre polynomials are the eigenvectors of an su_q(1|1)-representation

Deformed quantum mechanics and q-Hermitian operators

Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schr\"odinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which reproduces at the equilibrium the well-known q-deformed exponential stationary distribution. In this framework, q-deformed adjoint of an operator and q-hermitian operator properties occur in a natural way in order to satisfy the basic quantum mechanics assumptions.Comment: 10 page

Generalized thermodynamics of q-deformed bosons and fermions

We study the thermostatistics of q-deformed bosons and fermions obeying the symmetric algebra and show that it can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by an appropriate Jackson derivative. In this framework, we derive the most important thermodynamic functions describing the q-boson and q-fermion ideal gases in the thermodynamic limit. We also investigate the semi-classical limit and the low temperature regime and demonstrate that the nature of the q-deformation gives rise to pure quantum statistical effects stronger than undeformed boson and fermion particles.Comment: 8 pages, Physical Review E in pres

High-Temperature Expansions of Bures and Fisher Information Priors

For certain infinite and finite-dimensional thermal systems, we obtain --- incorporating quantum-theoretic considerations into Bayesian thermostatistical investigations of Lavenda --- high-temperature expansions of priors over inverse temperature beta induced by volume elements ("quantum Jeffreys' priors) of Bures metrics. Similarly to Lavenda's results based on volume elements (Jeffreys' priors) of (classical) Fisher information metrics, we find that in the limit beta -> 0, the quantum-theoretic priors either conform to Jeffreys' rule for variables over [0,infinity], by being proportional to 1/beta, or to the Bayes-Laplace principle of insufficient reason, by being constant. Whether a system adheres to one rule or to the other appears to depend upon its number of degrees of freedom.Comment: Six pages, LaTeX. The title has been shortened (and then further modified), at the suggestion of a colleague. Other minor change

q-Functional Wick's theorems for particles with exotic statistics

In the paper we begin a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the colored particles which appear in many problems of condensed matter physics, magnetism and quantum optics. Motivated by the general ideas of standard field theory we prove the q-functional analogues of Hori's formulation of Wick's theorems for the different ordered q-particle creation and annihilation operators. The formulae have the same formal expressions as fermionic and bosonic ones but differ by a nature of fields. This allows us to derive the perturbation series for the theory and develop analogues of standard quantum field theory constructions in q-functional form.Comment: 15 pages, LaTeX, submitted to J.Phys.

Unitarizable Representations of the Deformed Para-Bose Superalgebra Uq[osp(1/2)] at Roots of 1

The unitarizable irreps of the deformed para-Bose superalgebra $pB_q$, which is isomorphic to $U_q[osp(1/2)]$, are classified at $q$ being root of 1. New finite-dimensional irreps of $U_q[osp(1/2)]$ are found. Explicit expressions for the matrix elements are written down.Comment: 19 pages, PlainTe