Quantum signatures of the classical topological nonconnectivity threshold

A quantum Heisenberg model with anisotropic coupling and all-to-all interaction has been analyzed using the Bose-Einstein statistics. In F. Borgonovi, G. L. Celardo, M. Maianti, and E. Pedersoli, J. Stat. Phys. 116, 1435 (2004), the existence of a disconnection in the classical phase space has been proved analytically. Such topological disconnection occurs when the energy exceeds a suitable threshold value, called the topological nonconnectivity threshold. We address here the problem of finding quantum signatures of such a threshold. An independent definition of the quantum nonconnectivity threshold, motivated by considerations strictly valid in the quantum regime, is given. We also discuss the dynamical relevance of the quantum border with respect to the quantum magnetic reversal. Contrary to the classical case the magnetization can flip even below the classical threshold through macroscopic quantum tunneling. We evaluate the time scale for magnetic reversal from statistical and spectral properties for a small number of particles and in the semiclassical limit.