 9978 S. De Bievre, J.V. Pule
 Propagating edge states for a magnetic Hamiltonian
(94K, Latex 2e, 1 Postscript figure)
Mar 16, 99

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Abstract. We study the quantum mechanical motion of a charged particle moving in a half
plane (x>0) subject to a uniform constant magnetic field B directed along the
zaxis and to an arbitrary impurity potential W_B, assumed to be weak in the
sense that W_B_\infty < \delta B, for some \delta small enough. We show
rigorously a phenomenon pointed out by Halperin in his work on the quantum Hall
effect, namely the existence of current carrying and extended edge states in
such a situation. More precisely, we show that there exist states propagating
with a speed of size B^{1/2} in the ydirection, no matter how fast W_B
fluctuates. As a result of this, we obtain that the spectrum of the Hamiltonian
is purely absolutely continuous in a spectral interval of size \gamma B (for
some \gamma <1) between the Landau levels of the unperturbed system (i.e. the
system without edge or potential), so that the corresponding eigenstates are
extended.
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