32 research outputs found
Anyonic behavior of quantum group gases
We first introduce and discuss the formalism of -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 . We show
that quantum group gases exhibit anyonic behavior in and spatial
dimensions. In particular, for a boson gas at the parameter
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 and the number of spatial dimensions
. In addition, we consider a fourth-order interaction in the quantum group
fields , 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
An approach is proposed enabling to effectively describe the behaviour of a
bosonic system. The approach uses the quantum group formalism. In
effect, considering a bosonic Hamiltonian in terms of the
generators, it is shown that its thermodynamic properties are connected to
deformation parameters and . For instance, the average number of
particles and the pressure have been computed. If is fixed to be the same
value for , 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 .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 , which
is isomorphic to , are classified at being root of 1. New
finite-dimensional irreps of are found. Explicit expressions
for the matrix elements are written down.Comment: 19 pages, PlainTe