88 research outputs found
Statistical Mechanics of -Bosons in Dimensions
This paper is concerned with statistical properties of a gas of -bosons
without interaction. Some thermodynamical functions for such a system in
dimensions are derived. Bose-Einstein condensation is discussed in terms of the
parameters and . Finally, the second-order correlation function of a gas
of photons is calculated.Comment: 12 pages, revised Tex File (some fonts were changed
Non-Invariant Ground States, Thermal Average, and generalized Fermionic Statistics
We present an approach to generalised fermionic statistics which relates the
existence of a generalised statistical behaviour to non-invariant ground
states. Considering the thermal average of an operatorial generalization of the
Heisenberg algebra, we get an occupation number which depends on the degree of
mixing between symmetric and antisymmetric sectors of the ground state. A
natural prescription is given for the construction of a supersymmetric
statistics. We also show that the structure of the vacuum, and therefore the
statistical behaviour of the system, can be accounted for in terms of a second
order phase transition.Comment: 11 pages, accepted in Physics Letters
Quantum state transfer in a q-deformed chain
We investigate the quantum state transfer in a chain of particles satisfying
q-deformed oscillators algebra. This general algebraic setting includes the
spin chain and the bosonic chain as limiting cases. We study conditions for
perfect state transfer depending on the number of sites and excitations on the
chain. They are formulated by means of irreducible representations of a quantum
algebra realized through Jordan-Schwinger maps. Playing with deformation
parameters, we can study the effects of nonlinear perturbations or interpolate
between the spin and bosonic chain.Comment: 13 pages, 4 figure
Deformed Heisenberg algebra with reflection
A universality of deformed Heisenberg algebra involving the reflection
operator is revealed. It is shown that in addition to the well-known
infinite-dimensional representations related to parabosons, the algebra has
also finite-dimensional representations of the parafermionic nature. We
demonstrate that finite-dimensional representations are representations of
deformed parafermionic algebra with internal Z_2-grading structure. On the
other hand, any finite- or infinite-dimensional representation of the algebra
supply us with irreducible representation of osp(1|2) superalgebra. We show
that the normalized form of deformed Heisenberg algebra with reflection has the
structure of guon algebra related to the generalized statistics.Comment: 16 pages, LaTeX, to appear in Nucl. Phys.
Obstruction Results in Quantization Theory
We define the quantization structures for Poisson algebras necessary to
generalise Groenewold and Van Hove's result that there is no consistent
quantization for the Poisson algebra of Euclidean phase space. Recently a
similar obstruction was obtained for the sphere, though surprising enough there
is no obstruction to the quantization of the torus. In this paper we want to
analyze the circumstances under which such obstructions appear. In this context
we review the known results for the Poisson algebras of Euclidean space, the
sphere and the torus.Comment: 34 pages, Latex. To appear in J. Nonlinear Scienc
Three dimensional quadratic algebras: Some realizations and representations
Four classes of three dimensional quadratic algebras of the type \lsb Q_0 ,
Q_\pm \rsb , \lsb Q_+ , Q_- \rsb ,
where are constants or central elements of the algebra, are
constructed using a generalization of the well known two-mode bosonic
realizations of and . The resulting matrix representations and
single variable differential operator realizations are obtained. Some remarks
on the mathematical and physical relevance of such algebras are given.Comment: LaTeX2e, 23 pages, to appear in J. Phys. A: Math. Ge
New q-deformed coherent states with an explicitly known resolution of unity
We construct a new family of q-deformed coherent states , where . These states are normalizable on the whole complex plane and continuous
in their label . They allow the resolution of unity in the form of an
ordinary integral with a positive weight function obtained through the analytic
solution of the associated Stieltjes power-moment problem and expressed in
terms of one of the two Jacksons's -exponentials. They also permit exact
evaluation of matrix elements of physically-relevant operators. We use this to
show that the photon number statistics for the states is sub-Poissonian and
that they exhibit quadrature squeezing as well as an enhanced signal-to-quantum
noise ratio over the conventional coherent state value. Finally, we establish
that they are the eigenstates of some deformed boson annihilation operator and
study some of their characteristics in deformed quantum optics.Comment: LaTeX, 26 pages, contains 9 eps figure
An Algebraic q-Deformed Form for Shape-Invariant Systems
A quantum deformed theory applicable to all shape-invariant bound-state
systems is introduced by defining q-deformed ladder operators. We show these
new ladder operators satisfy new q-deformed commutation relations. In this
context we construct an alternative q-deformed model that preserve the
shape-invariance property presented by primary system. q-deformed
generalizations of Morse, Scarf, and Coulomb potentials are given as examples
Generally Deformed Oscillator, Isospectral Oscillator System and Hermitian Phase Operator
The generally deformed oscillator (GDO) and its multiphoton realization as
well as the coherent and squeezed vacuum states are studied. We discuss, in
particular, the GDO depending on a complex parameter q (therefore we call it
q-GDO) together with the finite dimensional cyclic representations. As a
realistic physical system of GDO the isospectral oscillator system is studied
and it is found that its coherent and squeezed vacuum states are closely
related to those of the oscillator. It is pointed out that starting from the
q-GDO with q root of unity one can define the hermitian phase operators in
quantum optics consistently and algebraically. The new creation and
annihilation operators of the Pegg-Barnett type phase operator theory are
defined by using the cyclic representations and these operators degenerate to
those of the ordinary oscillator in the classical limit q->1.Comment: 21 pages, latex, no figure
The quantum superalgebra : deformed para-Bose operators and root of unity representations
We recall the relation between the Lie superalgebra and para-Bose
operators. The quantum superalgebra , defined as usual in terms
of its Chevalley generators, is shown to be isomorphic to an associative
algebra generated by so-called pre-oscillator operators satisfying a number of
relations. From these relations, and the analogue with the non-deformed case,
one can interpret these pre-oscillator operators as deformed para-Bose
operators. Some consequences for (Cartan-Weyl basis,
Poincar\'e-Birkhoff-Witt basis) and its Hopf subalgebra are
pointed out. Finally, using a realization in terms of ``-commuting''
-bosons, we construct an irreducible finite-dimensional unitary Fock
representation of and its decomposition in terms of
representations when is a root of unity.Comment: 15 pages, LaTeX (latex twice), no figure
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