Frank, Rupert L. and Larson, Simon (2021) On the spectrum of the Kronig-Penney model in a constant electric field. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20211004-232828060
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Abstract
We are interested in the nature of the spectrum of the one-dimensional Schrödinger operator −d²/dx² − Fx + ∑_(n∈ℤ) g_nδ(x−n)in L²(ℝ) with F > 0 and two different choices of the coupling constants {g_n}n ∈ ℤ. In the first model g² ≡ λ and we prove that if F ∈ π²ℚ then the spectrum is ℝ and is furthermore absolutely continuous away from an explicit discrete set of points. In the second model g_n are independent random variables with mean zero and variance λ². Under certain assumptions on the distribution of these random variables we prove that almost surely the spectrum is ℝ and it is dense pure point if F < λ²/2 and purely singular continuous if F > λ²/2.
Item Type: | Report or Paper (Discussion Paper) | ||||||||
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Additional Information: | © 2021 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. U.S. National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.) and Knut and Alice Wallenberg Foundation grant KAW 2018.0281 (S.L.) are acknowledged. | ||||||||
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Record Number: | CaltechAUTHORS:20211004-232828060 | ||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20211004-232828060 | ||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
ID Code: | 111207 | ||||||||
Collection: | CaltechAUTHORS | ||||||||
Deposited By: | George Porter | ||||||||
Deposited On: | 07 Oct 2021 19:14 | ||||||||
Last Modified: | 07 Oct 2021 19:14 |
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