Motivated by the experimental observation of resonant tunneling in systems of half-integer spin, such as V15 and Mn4, we study the mechanism of the adiabatic change of the magnetization in systems with time-reversal symmetry. Although tunneling between the degenerate ground states is suppressed in a simple Kramers doublet, some types of perturbational interactions cause an avoided level crossing structure in the energy level structures when the system possesses additional degeneracy of the ground state. We show that a nonadiabatic transition governed by the Landau-Zener-Stückelberg mechanism occurs in many cases, and also find more general cases of adiabatic change of the magnetization in which LZS mechanism cannot be applied directly.
The system under consideration is an
N-particle quantum-mechanical system enclosed in a volume
V, in which the particles interact via two-body hard-sphere potentials, with hard-sphere diameter
a. The two-body hard-sphere problem is first discussed by a generalization of Fermi's pseudopotential by means of which the problem is formulated entirely in terms of the scattering phase shifts. It is then shown that a pseudopotential for the
N-body problem can be introduced, and leads to an expansion of the energy levels of the system in powers of
a. The first order energy levels of a Bose and a Fermi system are calculated. For the Bose system, the first order energy formula exhibits an "energy gap" above the ground state, leading to properties of the system not dissimilar to that of a superfluid. The ground state energy for a Bose system is calculated to order
a3 and that for the Fermi system, to order
a2. The physical interpretation and validity of these results are discussed.
The level spacing of the Bassichis-Foldy model of an interacting boson system is studied as a function of the coupling F between the two levels of opposite momenta. For a specific value of this coupling F=
FT, the ground state of the system becomes degenerate, and the histogram of the energy differences between neighboring levels shows a sharp peak near the origin. The dependence of the energy levels corresponding to the minimum spacing on F follows the classical separatrix energy for a wide range of the parameters of the system, except when F approaches
FT. Around
FT the ground-state energy changes very rapidly as a function of F unlike the slow variation of the classical separatrix energy. By studying the classical description of the motion in terms of the action-angle variables, one can show an additional symmetry of the Hamiltonian for F very close to
FT. Thus, in this model the nonlinear classical Hamiltonian can be used as an indicator of the degeneracy of the system, even though the quantum-mechanical system does not have the symmetry of the classical problem.