49 research outputs found
A Generalization of Haldane state-counting procedure and -deformations of statistics
We consider the generalization of Haldane's state-counting procedure to
describe all possible types of exclusion statistics which are linear in the
deformation parameter . The statistics are parametrized by elements of the
symmetric group of the particles in question. For several specific cases we
determine the form of the distribution functions which generalizes results
obtained by Wu. Using them we analyze the low-temperature behavior and
thermodynamic properties of these systems and compare our results with previous
studies of the thermodynamics of a gas of -ons. Various possible physical
applications of these constructions are discussed.Comment: 17 pages, latex, 6 figures small corrections were made, reference and
acknowledgments are adde
Generalization of Agranovich-Toshich transformation and constraint free bosonic representation for systems of truncated oscillators
The generalization of Agranovich-Toshich representation of paulion operators
in terms of bosonic ones for the case of truncated oscillators of higher ranks
is represented. We use this generalization to introduce a new constraint free
bosonic description of truncated oscillator systems. The corresponding
functional integral representations for thermodynamic quantities are given and
the application to investigations of Long Rang Order in the system is
discussed.Comment: latex, 8 pages, no figure
Ansatz from Non-Linear Optics Applied to Trapped Bose-Einstein Condensates
A simple analytical ansatz, which has been used to describe the intensity
profile of the similariton laser (a laser with self-similar propagation of
ultrashort pulses), is used as a variational wave function to solve the
Gross-Pitaevskii equation for a wide range of interaction parameters. The
variational form interpolates between the noninteracting density profile and
the strongly interacting Thomas-Fermi profile smoothly. The simple form of the
ansatz is modified for both cylindrically symmetric and completely anisotropic
harmonic traps. The resulting ground-state density profile and energy are in
very good agreement with both the analytical solutions in the limiting cases of
interaction and the numerical solutions in the intermediate regime.Comment: 4 pages, 3 figures, published versio
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.
Generalized Grassmannian Coherent States For Pseudo-Hermitian Level Systems
The purpose of this paper is to generalize fermionic coherent states for
two-level systems described by pseudo-Hermitian Hamiltonian \cite{Trifonov}, to
n-level systems. Central to this task is the expression of the coherent states
in terms of generalized Grassmann variables. These kind of Grassmann coherent
states satisfy bi-overcompleteness condition instead of over-completeness one,
as it is reasonably expected because of the biorthonormality of the system.
Choosing an appropriate Grassmann weight function resolution of identity is
examined. Moreover Grassmannian coherent and squeezed states of deformed group
for three level pseudo-Hermitian system are presented.Comment: 17 page