Abstract:
In this work we consider three examples of random singular perturbations in multi-dimensional models of waveguides. These perturbations are described by a large potential supported on a set of a small measure, by a compactly supported fast oscillating potential, and by a delta-potential. In all cases we prove initial length scale estimate.
Keywords:
random operator, initial length scale estimate, perturbation, small parameter, spectral localization.
Citation:
D.I. Borisov, R. Kh. Karimov, T. F. Sharapov, “Initial length scale estimate for waveguides with some random singular potentials”, Ufa Math. J., 7:2 (2015), 33–54
\Bibitem{BorKarSha15}
\by D.I.~Borisov, R.~Kh.~Karimov, T.~F.~Sharapov
\paper Initial length scale estimate for waveguides with some random singular potentials
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 2
\pages 33--54
\mathnet{http://mi.mathnet.ru/eng/ufa277}
\crossref{https://doi.org/10.13108/2015-7-2-33}
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Linking options:
https://www.mathnet.ru/eng/ufa277
https://doi.org/10.13108/2015-7-2-33
https://www.mathnet.ru/eng/ufa/v7/i2/p35
This publication is cited in the following 6 articles:
Khusnullin I.Kh., “On Perturbation of the Schrodinger Operator With a Localized Complex-Valued Potential”, Azerbaijan J. Math., 11:1 (2021), 104–117
D. Borisov, F. Hoecker-Escuti, I. Veselic, “Expansion of the spectrum in the weak disorder regime for random operators in continuum space”, Commun. Contemp. Math., 20:1 (2018), 1750008
D. I. Borisov, “Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf”, J. Math. Sci. (N. Y.), 252:2 (2021), 135–146
A. R. Bikmetov, I. Kh. Khusnullin, “Perturbation of Hill operator by narrow potentials”, Russian Math. (Iz. VUZ), 61:7 (2017), 1–10
I. Kh. Khusnullin, “Vozmuschenie volnovoda uzkim potentsialom”, Tr. IMM UrO RAN, 23, no. 2, 2017, 274–284
A. R. Bikmetov, V. F. Vil'danova, I. Kh. Khusnullin, “On perturbation of a Schrödinger operator on axis by narrow potentials”, Ufa Math. J., 7:4 (2015), 24–31
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