 9494 Alexander MOROZ
 SINGLEPARTICLE DENSITY OF STATES FOR THE AHARONOVBOHM POTENTIAL
AND INSTABILITY OF MATTER WITH ANOMALOUS MAGNETIC MOMENT IN 2+1
DIMENSIONS
(25K, latex)
Apr 18, 94

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Abstract. In the nonrelativistic case we find that whenever the relation
$mc^2/e^2 <X(\al,g_m)$ is satisfied, where $\al$ is a flux
in the units of the flux quantum, $g_m$ is magnetic moment,
and $X(\al,g_m)$ is some function that is nonzero only for
$g_m>2$ (note that $g_m=2.00232$ for the electron),
then the matter is unstable against formation of the flux $\al$.
The result persists down to $g_m=2$ provided the AharonovBohm
potential is supplemented with a short range attractive potential.
We also show that whenever a bound state is present in the spectrum it
is always accompanied by a resonance with the energy proportional to
the absolute value of the binding energy.
In the relativistic case the instability along with
the resonance disappear as long as the minimal coupling is
considered. For the KleinGordon equation with the Pauli coupling
which exists in (2+1) dimensions without any reference to a spin
the matter is again unstable for $g_m>2$.
The results are obtained by calculating the change of the density of states
induced by the AharonovBohm potential. The KreinFriedel formula for this
longranged potential is shown to be valid when supplemented with zeta
function regularization.
PACS : 03.65.Bz, 0370.+k, 0380.+r, 05.30.Fk
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