Applications of Classical and Quantum Algebras to Molecular Thermodynamics

Details Applications of Classical and Quantum Algebras to Molecular Thermodynamics Applications of Classical and Quantum Algebras to Molecular Thermodynamics

2002-01-15

arxiv.org/abs/cond-mat/0201240v1

Physics

Condensed Matter

Statistical Mechanics

LATEX2e, 12 pages, 2 figures. Plenary talk given at the IX International Conference on Symmetry Methods in Physics, Yerevan, A

Scientific paper

Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A vibrational high-temperature partition function and the related thermodynamic potentials are derived in terms of the parameters of the model. Quantum analogues of anharmonic bosons, $q$-bosons, are introduced and used to describe anharmonic properties of molecules and solids. It is shown that the quantum deformation parameter is related to the fixed number of anharmonic bosons and the shape of the anharmonic potential. A new algebraic realization of the $q$-bosons, for the case of $q$ being a root of unity is given. This realization represents the symmetry of a linear lattice with periodic boundary conditions.

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