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

E. M. F. Curado·M. A. Rego-Monteiro
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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.

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E. M. F. Curado, M. A. Rego-Monteiro. 2000-06-14. Thermodynamic Properties of a Solid Exhibiting the Energy Spectrum given by the Logistic Map. https://doi.org/10.1103/physreve.61.6255

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