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Magnetic Susceptibility in the Aharonov-Bohm Experiment
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T. M. Hong and F. R. Lee
Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 300, R.O.C. (Received July 16, 1997) |
We study the magnetization M and the magnetic susceptibility
of both an electron and many ideal electrons on a ring and a more
realistic hollow disk for the Aharonov-Bohm experiment. That is, how
does the electron respond to the change of a nontrivial vector
potential when the magnetic field is zero? Numerical results of M(T)
and 
for the ring case are supported by analytic expressions.
Similar analytic expressions for the disk are only possible when we
assume, based on the qualitative resemblance of its numerical results
with the ring case, the eigenenergies are separable into radial and
angular parts. Although this approximation is only justified rigorously
when the disk is narrow, numerical results provides evidence to extend
its validity to even a wide disk as long as the electron number is not
too large.
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