Thermodynamic Properties of a Solid Exhibiting the Energy Spectrum given by the Logistic Map
arXiv:cond-mat/0006238 · doi:10.1103/PhysRevE.61.6255
Abstract
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.
15 pages, 7 EPS figures, Latex
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