Simple Applications of q-Bosons

Details Simple Applications of q-Bosons Simple Applications of q-Bosons

2001-05-09

arxiv.org/abs/cond-mat/0105193v2

J. Phys. A34 (2001) L503-L509

Physics

Condensed Matter

Statistical Mechanics

LATEX2e, 10 pages, v2: few misprints corrected, added Journal-ref

Scientific paper

10.1088/0305-4470/34/37/101

A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which is a generalisation of the Heisenberg-Weyl algebra obtained by introducing a deformation parameter $q$. Further, we present a new algebraic realization of the $q$-bosons, for the case of $q$ being a root of unity, which corresponds to a periodic structure described by a finite-dimensional representation. We show that this structure represents the symmetry of a linear lattice with periodic boundary conditions.

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