Thermodynamic Properties of a Solid Exhibiting the Energy Spectrum given by the Logistic Map

Details Thermodynamic Properties of a Solid Exhibiting the Energy Spectrum given by the Logistic Map Thermodynamic Properties of a Solid Exhibiting the Energy Spectrum given by the Logistic Map

2000-06-14

arxiv.org/abs/cond-mat/0006238v1

Phys. Rev. E 61 (2000) 6255

Physics

Condensed Matter

Statistical Mechanics

15 pages, 7 EPS figures, Latex

Scientific paper

10.1103/PhysRevE.61.6255

We show that the infinite-dimensional representation of the recently introduced Logistic algebra can be interpreted as a non-trivial generalization of the Heisenberg or oscillator algebra. This allow us to construct a quantum Hamiltonian having the energy spectrum given by the logistic map. We analyze the Hamiltonian of a solid whose collective modes of vibration are described by this generalized oscillator and compute the thermodynamic properties of the model in the two-cycle and r=3.6785 chaotic region of the logistic map.

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