 95148 Alexander MOROZ
 THE SINGLEPARTICLE DENSITY OF STATES, BOUND STATES, PHASESHIFT FLIP,
AND A RESONANCE IN THE PRESENCE OF AN AHARONOVBOHM 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 AharonovBohm potential are analyzed and the singleparticle
density of states for different selfadjoint extensions
is calculated. The singleparticle 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 KreinFriedel formula for this longranged 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 spindown 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 AharonovCasher 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 phaseshift 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 onehalf 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 switchedon. Several suggestions for new experiments are
given.
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