Marcelo R. Ubriaco

ANYONIC BEHAVIOR OF QUANTUM GROUP GASES

We first introduce and discuss the formalism of SU{sub q}(N) bosons and fermions and consider the simplest Hamiltonian involving these operators. We then calculate the grand partition function for these models and study the high temperature (low density) case of the corresponding gases for N=2. We show that quantum group gases exhibit anyonic behavior in D=2 and 3 spatial dimensions. In particular, for a SU{sub q}(2) boson gas at D=2 the parameter q interpolates within a wider range of attractive and repulsive systems than the anyon statistical parameter. {copyright} {ital 1997} {ital The American Physical Society}

THERMODYNAMICS OF A FREE SUQ(2) FERMIONIC SYSTEM

Abstract We calculate the partition function, average occupation number and internal energy for an SU q (2) fermionic system and compare this model at T = 0 with the ordinary fermionic, q = 1, case. At low temperatures and q ⪢ 1 we find the chemical potential μ to have the same temperature dependence as the Fermi case. For q ⪡ 1, the function μ ( T ) has in addition a linear dependence on T .

HIGH AND LOW TEMPERATURE BEHAVIOR OF A QUANTUM GROUP FERMION GAS

We consider the simplest SUq(2) invariant fermionic Hamiltonian and calculate the low and high temperature behavior for the two distinct cases q>1 and q<1. For low temperatures we find that entropy values for the Fermi case are an upper bound for those corresponding to q≠1. At high temperatures we find that the sign of the second virial coefficient depends on q, and vanishes at q=1.96. An important consequence of this fact is that the parameter q connects the fermionic and bosonic regions, showing therefore that SUq(2) fermions exhibit fractional statistics in three spatial dimensions.

Bose-Einstein condensation of a quantum group boson gas

We study the Bose-Einstein condensation of a gas with

Variational extensions of the mean spherical approximation

SU_q(2)

QUANTUM GROUP SCHRÖDINGER FIELD THEORY

symmetry. We show, in the thermodynamic limit, that the boson interactions introduced by the quantum group symmetries enhance Bose-Einstein condensation giving a discontinuity in the heat capacity

Time evolution in quantum mechanics on the quantum line

C_v

Correlation functions in the factorization approach of nonextensive quantum statistics

at the critical temperature

COMPLEX q-ANALYSIS AND SCALAR FIELD THEORY ON A q-LATTICE

T_c

Quantum group invariant, nonextensive quantum statistical mechanics

. The critical temperature and the gap in