J.-M. Combes, P. D. Hislop, E. Soccorsi
Edge states for quantum Hall Hamiltonians
(232K, Postscript)

ABSTRACT.  The study of the quantum motion of a charged particle 
in a half-plane as well as in an infinite strip 
submitted to a perpendicular constant magnetic 
field $B$ reveals eigenstates propagating permanently 
along the edge, the so-called 
edge states. Moreover, in the 
half-plane geometry, current carried by edge states 
with energy in between the Landau levels persists in the 
presence of a perturbing 
potential small relative to B. 
We show here that edge states carrying current survive 
in an infinite strip for a long time before 
tunneling between the two edges has a destructive effect on it. The proof 
relies on 
Helffer-Sj\"ostrand functional calculus and decay properties of 
quantum Hall Hamiltonian resolvent.