We consider a Zener double-well problem related to the magnetic bands in a superlattice Bloch operator. We give the precise asymptotic behaviour of the level splittings. This way we extend the Peierls substitution rule to an exponentially small term and furthermore, for the first time, we rigorously compute an exponentially small term in a Zener problem.
Asymptotics of Zener double-well splittings and magnetic gaps / V., Grecchi; Sacchetti, Andrea. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - STAMPA. - 27:(1994), pp. 1393-1399.
Asymptotics of Zener double-well splittings and magnetic gaps
SACCHETTI, Andrea
1994
Abstract
We consider a Zener double-well problem related to the magnetic bands in a superlattice Bloch operator. We give the precise asymptotic behaviour of the level splittings. This way we extend the Peierls substitution rule to an exponentially small term and furthermore, for the first time, we rigorously compute an exponentially small term in a Zener problem.
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