Thermodynamic properties of a solid exhibiting the energy spectrum given by the logistic map
We show that the infinite-dimensional representation of the recently introduced logistic algebra can be interpreted as a nontrivial generalization of the Heisenberg or oscillator algebra. This allows 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.
Curado
EM
Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil.
Rego-Monteiro
MA