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

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.