SingleParticle Density of States for the AharonovBohm Potential and Instability of Matter with Anomalous Magnetic Moment in 2+1 Dimensions
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. 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
 Publication:

arXiv eprints
 Pub Date:
 April 1994
 arXiv:
 arXiv:hepth/9404104
 Bibcode:
 1994hep.th....4104M
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter
 EPrint:
 (sign change in Eq.'s (3031), 2 references added) 11pp. plain latex, IPNO/TH 9420