We derive the frequency-dependent conductance of an ideal finite conductor in the presence of a weak magnetic field. As a model we use a tight-binding Hamiltonian. It is shown that the conductance as a function of the Fermi energy and the magnetic field is quantised. As a function of the frequency and the length of the system the conductance shows oscillatory behaviour.
The effect of tetragonal splitting of the electronic doublet on the properties of the cubic E 8 E Jahn-Teller system is investigated taking account only of linear Jahn-Teller coupling, Ham reduction factors appropriate to the tetragonal symmetry are introduced, and their connection with the cubic reduction factors is established. A simple relation between the vibronic matrix elements of vibrational and electronic operators is derived. Numerical calculations are performed for weak to intermediate Jahn-Teller coupling where the electronic splitting competes with the Jahn-Teller interaction. The vibronic ground doublet is studied in detail. It is found that the reduction factor corresponding to q can drop below + considerably. Experimental consequences for electron paramagnetic resonance on a 2E state in a tetragonal field and for Mossbauer spectroscopy on a 'E state split by magnetic exchange are discussed. The theory predicts the spectra to be markedly different from what is expected either for a tetragonal purely electronic state or for a cubic Jahn-Teller coupled state.
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