Statistics of q-oscillators, quons and relations to fractional statistics

Abstract

The statistics of q-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic q-oscillators are found for their corresponding Fock space representations in the case when the hamiltonian is identified with the number operator. In this case and for nonrelativistic particles, the single-particle temperature Green function is defined with q-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic q-gases in an arbitrary space dimension are found near Bose statistics, as well as the one for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated. The phenomenon of Bose-Einstein condensation in the q-deformed gases is also discussed. * ) ICSC

Miscellaneous Applications of Quons

“…We may ask the question: Is it easier to find solutions of (17), (18) than to find solutions of (19), (20)? We do not have any answer.…”

“…We do not have any answer. In the case of MUBs, we have a general solution (see Proposition 3) of (19) and thus (17) for d prime in the framework of angular momentum theory. It would be interesting to extend this result for d a power of a prime.…”

Geometric Aspects and Some Uses of Deformed Models of Thermostatistics

“…In this paper, we focus on theoretical, geometric and applied aspects of DBGMs. Though the deformed models are under study from early nineties, see, e.g., [1][2][3][4][5][6][7], their investigation still continues, and a number of diverse DBGMs' applications in several directions of physics were found. These include: description of the properties of phonon spectrum in 4 He [8]; physics of excitons [9]; usage of nonstandard statistics and DBGMs in the physics of black holes and dark matter [10][11][12][13][14]; attempts to explain the observed non-Bose features of pions shown by π π-correlations in the RHIC/STAR experiments (see, e.g., [15]).…”

Generalized exclusion and Hopf algebras

“…For example the q-deformed harmonic oscillators at roots unity is connected with two anyon system [8]. Different versions of the deformation of oscillator algebras and their use in physics can be found in the review [9] and the connection of between q-deformed structures and fractional statistics can be found in [10]. In terms of creation and annihilation operators the generalized exclusion can be expressed as a k = 0 and (a † ) k = 0.…”