Acta mathematica scientia, Series B >
CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT
Received date: 2011-10-08
Online published: 2011-11-20
Supported by
This research was supported by the Israel Science Foundation.
We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge. In the semi-classical limit h ! 0 these eigenstates concentrate near a maximizer of the scalar potential of the associated Schr¨odinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.
Key words： Schr¨odinger equation; gauge; semi classical limit; Bloch eigenstate
Gershon Wolansky . CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT[J]. Acta mathematica scientia, Series B, 2011 , 31(6) : 2278 -2284 . DOI: 10.1016/S0252-9602(11)60399-8
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