Quantum-classical correspondence in energy space: Two interacting spin particles

Abstract

The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy. Main attention is paid to the structure of chaotic eigenfunctions (EF) and to the local spectral density of states (LDOS). A remarkable correspondence has been found for the shapes of EF and LDOS in the energy representation, to their classical counterparts. Comparison with the Band Random Matrix theory predictions has revealed quite significant differences which are due to dynamical nature of the model. On the other hand, a partial agreement is found by inserting randomness `` ad hoc '' in the dynamical model for two-body matrix elements. This shows that, at least for small number of particles, care must be taken when classical correlations are neglected. The question of quantum localization in the energy space is discussed both for dynamical and random model.