Related papers: Intermediate statistics as a consequence of deform…
The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra has been an outstanding issue. This original concept introduced long ago by Greenberg is the motivation for this investigation. We…
Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying…
General permutation invariant statistics in the second quantized approach are considered. Simple interpolations between dual statistics are constructed. Particularly, we present a new minimal interpolation between parabosons and…
The simple algebras of a dressed operator, which is composed of a dressing and a residual operators, are averaged following a proper statistics of the dressing one. In the Bose-Einstein statistics, a (fermionic) Calogero-Vasiliev…
Motivated by fractional quantum Hall effects, we introduce a universal space of statistics interpolating Bose-Einstein statistics and Fermi-Dirac statistics. We connect the interpolating statistics to umbral calculus and use it as a bridge…
Once again the possibility of the existence of particle statistics intermediate between those of Fermi-Dirac and Bose-Einstein surfaces. Here attention is drawn to the fact that some fifteen years ago it was shown that such so-called…
In this paper, we first discuss the general properties of an intermediate-statistics quantum bracket, $[ u,v]_{n}=uv-e^{i2\pi /(n+1)}vu$, which corresponds to intermediate statistics in which the maximum occupation number of one quantum…
We present a theory of particles, obeying intermediate statistics ("anyons"), interpolating between Bosons and Fermions, based on the principle of Detailed Balance. It is demonstrated that the scattering probabilities of identical particles…
Gentile statistics describes fractional statistical systems in the occupation number representation. Anyon statistics researches those systems in the winding number representation. Both of them are intermediate statistics between…
In this paper, we show that spin waves, the elementary excitation of the Heisenberg magnetic system, obey a kind of intermediate statistics with a finite maximum occupation number n. We construct an operator realization for the intermediate…
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…
An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be…
Generalized quons interpolating between Bose, Fermi, para-Bose, para-Fermi, and anyonic statistics are proposed. They follow from the R-matrix approach to deformed associative algebras. It is proved that generalized quons have the same main…
This paper presents a new way to construct single-valued many-body wavefunctions of identical particles with intermediate exchange phases between Fermi and Bose statistics. It is demonstrated that the exchange phase is not a representation…
Using deformed Green's oscillators and Green's Ansatz,we construct a multiparameter interpolation between para-Bose and para-Fermi statistics of a given order. When the interpolating parameters $q_{ij}$ satisfy $|q_{ij}|<1 (|q_{ij}|= 1)$,…
We first reobtain in a simpler way the Haldane fractional statistics at thermal equilibrium using an interpolation argument. We then show that the mean occupation number for fractional statistics is invariant to a group of duality…
Operators, refered to as k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of two noncommuting quon algebras. The deformation parameters for these quon algebras are roots of…
We overwiev the properties of a quantum gas of particles with the intermediate statistics defined by Haldane. Although this statistics has no direct connection to the symmetry of the multiparticle wave function, the statistical distribution…
Beyond Bose and Fermi statistics, there still exist various kinds of generalized quantum statistics. Two ways to approach generalized quantum statistics: (1) in quantum mechanics, generalize the permutation symmetry of the wave function and…
We study the thermodynamics of a crystalline solid by applying intermediate statistics obtained by deforming known solid state models using the mathematics of $q$-analogs. We apply the resulting $q$-deformation to both the Einstein and…