THE SINGLE-PARTICLE DENSITY OF STATES AND THE RESONANCE IN THE AHARONOV–BOHM POTENTIAL

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Abstract
The single-particle densitity of states (DOS) for the Pauli and the Schrödinger Hamiltonians in the presence of an Aharonov–Bohm potential is calculated for different values of the particle magnetic moment. The DOS is a symmetric and periodic function of the flux. The Krein–Friedel formula can be applied to this long-ranged potential when regularized with the zeta function. We have found that whenever a bound state is present in the spectrum it is always accompanied by a resonance. The shape of the resonance is not of the Breit-Wigner type. The differential scattering cross section is asymmetric if a bound state is present and gives rise to the Hall effect. As an application, propagation of electrons in a dilute vortex limit is considered and the Hall resistivity is calculated.
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