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Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in R^3

Exner, Pavel and Frank, Rupert L. (2007) Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in R^3. Annales Henri Poincaré, 8 (2). pp. 241-263. ISSN 1424-0637. doi:10.1007/s00023-006-0307-3.

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We consider a model of leaky quantum wires in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded and periodically modulated along the line. We demonstrate that such a system has a purely absolutely continuous spectrum and its negative part has band structure with an at most finite number of gaps. This result is extended also to the situation when there is an infinite number of the lines supporting the perturbations arranged periodically in one direction.

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Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2007 Birkhäuser Verlag Basel/Switzerland. Submitted: August 29, 2005. Accepted: June 9, 2006. Communicated by Vincent Rivasseau. The research was supported in part by ASCR and its Grant Agency within the projects IRP AV0Z10480505 and A100480501. The second author acknowledges gratefully a partial support through the ESF SPECT programme.
Funding AgencyGrant Number
Ústav dějin umění Akademie věd ČRAV0Z10480505
Ústav dějin umění Akademie věd ČRA100480501
European Science FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20170601-083108196
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Official Citation:Exner, P. & Frank, R.L. Ann. Henri Poincaré (2007) 8: 241. doi:10.1007/s00023-006-0307-3
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77881
Deposited By: Ruth Sustaita
Deposited On:01 Jun 2017 21:03
Last Modified:15 Nov 2021 17:34

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