Anyonic behavior of quantum group gases

Abstract

We first introduce and discuss the formalism of $S{U}_q(N)$-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 $D=3$ spatial dimensions. In particular, for a $S{U}_q(2)$ boson gas at $D=2$ the parameter $q$ interpolates within a wider range of attractive and repulsive systems than the anyon statistical parameter.

LaTeX file, 19 pages, two figures ,uses epsf.sty

References in corpus (11)

• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• Thermodynamic q-Distributions That Aren't
• Quantum Group Gauge Theory on Classical Spaces
• Thermodynamics of a free $S{U}_q(2)$ fermionic system
• Dynamical Symmetries in q-deformed Quantum Mechanics
• High and low temperature behavior of a quantum group fermion gas
• SU_q(n) Gauge Theory
• U_q(N) Gauge Theories
• Quantum Group Schrödinger Field Theory
• The Canonical Partition Function for Quons
• Conservation of Statistics and Generalized Grassmann Numbers

Cited by in corpus (23)

• Quantum Groups and Their Applications in Nuclear Physics
• High temperature behavior of a deformed Fermi gas obeying interpolating statistics
• Bose-Einstein condensation of a quantum group gas
• A comparative study on q-deformed fermion oscillators
• An Algebraic q-Deformed Form for Shape-Invariant Systems
• Thermodynamics of bosons systems related to Dunkl differential-difference operators
• Virial coefficients in $(\tilde{\mu },q)$-Bose gas model related to compositeness of particles and their interaction: temperature-dependence problem
• Bose Einstein condensation in a gas of the Fibonacci oscillators
• Quantum groups as hidden symmetries of quantum impurities
• Non-extensive entropy of bosonic Fibonacci oscillators
• λ-transition in low dimensional systems with SU_q(2) symmetry
• Scalar curvature of systems with fractal distribution functions
• Analytical approach to the Bose polaron \\ via $q$-deformed Lie algebra
• Geometry of Quantum Group invariant systems
• Intermediate statistics: addressing the thermoelectric properties of solids
• Quantum group invariant, nonextensive quantum statistical mechanics
• High-Temperature Expansions of Bures and Fisher Information Priors
• Coupling q-deformed dark energy to dark matter
• Generalized Brans-Dicke theory from Verlinde's entropic gravity
• Solution of deformed Einstein equations and quantum black holes
• Interacting dark matter and q-deformed dark energy non-minimally coupled to gravity
• Remarks on SU_q(2) fermions
• Anyonic behavior of quantum group fermionic and bosonic systems