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arXiv:quant-ph/0407170 · Physica A Statistical Mechanics and its Applications

Quantum spin tunneling in a soluble quasi-spin model: an angle-based potential description

D. Galetti, B. M. Pimentel, C. L. Lima

Published Dec 30, 2004• 3 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2004.11.056

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Starting from a phenomenological Hamiltonian originally written in terms of angular momentum operators we derive a new quantum angle-based Hamiltonian that allows for a discussion on the quantum spin tunneling. The study of the applicability of the present approach, carried out in calculations with a soluble quasi-spin model, shows that we are allowed to use our method in the description of physical systems such as the Mn12-acetate molecule, as well as the octanuclear iron cluster, Fe8, in a reliable way. With the present description the interpretation of the spin tunneling is seen to be direct, the spectra and energy barriers of those systems are obtained, and it is shown that they agree with the experimental ones.
The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wigner function is written for some chosen states associated to discrete angle and angular momentum variables, and the time evolution is numerically calculated using the discrete von Neumann-Liouville equation. Direct evidences in the time evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU (2)-based semiclassical continuous approach to the Lipkin model is also presented.