Bose-Einstein condensation of a quon gas

Hui-yun Pan, Zu Sen Zhao, Haiyan Li

Stefan Kirchner

Thermodynamical properties of a model quon gas are reported. The quons considered are the objects obeying the deformed commutator aa†−qa†a=1 with −1⩽q⩽1. Although q=1 and q=−1 correspond respectively to boson and fermion statistics, it is not trivial to generate a quon gas which interpolates between the boson gas and the fermion gas without Pauli’s exclusion principle. The proposed model, interpolating between the two limits, can realize the Maxwell-Boltzmann limit at q=0 and simulate a free anyon gas. Under the restriction −1⩽q⩽1, the gas is deformed but bosonic in nature. It shows the Bose-Einstein condensation even in two dimensions.

Daniel F. Walls, Gerard J Milburn

Rajaram Nityananda

Akira Inomata

To understand possible physical consequences of quantum deformation, we investigate statistical behaviors of a quon gas. The quon is an object which obeys the minimally deformed commutator (or q-mutator): a\, a^{\dagger} - q a^{\dagger}a=1 with -1\leq q\leq 1. Although q=1 and q=-1 appear to correspond respectively to boson and fermion statistics, it is not easy to create a gas which unifies the boson gas and the fermion gas. We present a model which is able to interpolates between the two limits. The quon gas shows the Bose-Einstein condensation near the Boson limit in two dimensions.

W. S. Chung, Abdullah Algin

A q-deformed field theory at finite temperature is presented and its related thermo field dynamics is constructed. This enables us to introduce the quon field, whose Lagrangian leads to a q-deformed partition function. Accordingly, the general thermostatistical properties of a gas model of quon fields, such as the q-deformed statistical distribution function describing an intermediate-statistics behavior and the equation of state in two and three dimensions, are investigated. For low temperatures, the conditions under which Bose–Einstein-like condensation would occur in the quon gas model are discussed. It is shown that the critical temperature of such a gas is higher than that of the usual Bose gas for values of the model parameter q in the range [Formula: see text]. For high temperatures, possible anyonic behavior of the present quon gas model in two spatial dimensions is studied through an analysis of the effect of deformation on the second and third virial coefficients in the equation of state. The results obtained in this work reveal the ability of the model for analyzing a parastatistical behavior of systems with quasiparticles and put forward it as a possible candidate for effectively modeling the properties of some exotic quantum states, such as in the case of dark matter constituents.