95-148 Alexander MOROZ
THE SINGLE-PARTICLE DENSITY OF STATES, BOUND STATES, PHASE-SHIFT FLIP, AND A RESONANCE IN THE PRESENCE OF AN AHARONOV-BOHM POTENTIAL (273K, compressed postscript file, 66 pp.) Mar 16, 95
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Abstract. Both the nonrelativistic scattering and the spectrum in the presence of the Aharonov-Bohm potential are analyzed and the single-particle density of states for different self-adjoint extensions is calculated. The single-particle density of states is shown to be a symmetric and periodic function of the flux which depends only on the distance from the nearest integer. The Krein-Friedel formula for this long-ranged potential is shown to be valid when regularized with the zeta function. The limit when the radius $R$ of the flux tube shrinks to zero is discussed. For $R\neq 0$ and in the case of an anomalous magnetic moment $g_m>2$ (note, e.\ g., that $g_m=2.00232$ for the electron) the coupling for spin-down electrons is enhanced and bound states occur in the spectrum. Their number does depend on a regularization and generically does not match with the number of zero modes in a given field that occur when $g_m=2$. Provided the coupling with the interior of the flux tube is not renormalized to a critical one neither bound states nor zero modes survive the limit $R\rightarrow 0$. The Aharonov-Casher theorem on the number of zero modes is corrected for the singular field configuration. Whenever a bound state does survive the $R\rightarrow 0$ limit it is always accompanied by a resonance. The presence of a bound state manifests itself in the asymmetric differential scattering cross section that can give rise to the Hall effect. The Hall resistivity is calculated in the dilute vortex limit. The magnetic moment coupling and not the spin is shown to be the primary source for the phase-shift flip that may occur even in its absence. The total energy of the system consisting of particles and field is discussed. An application to persistent currents in the plane for both spinless and spin one-half fermions is given. Persistent currents are also predicted to exist in the field of a cosmic string. The $2nd$ virial coefficient of anyons with a short range delta function interaction is calculated. The coefficient is shown to be remarkably stable when such an interaction is switched-on. Several suggestions for new experiments are given.

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