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Resolvent expansions for the Schrodinger operator on the discrete half-line

English (英語)

Journal of Mathematical Physics

58(5)

052101-052101

AIP Publishing

2017-05

2018-06-01

Simplified models of transport in mesoscopic systems are often based on a small sample connected to a finite number of leads. The leads are often modelled using the Laplacian on the discrete half-line N. Detailed studies of the transport near thresholds require detailed information on the resolvent of the Laplacian on the discrete half-line. This paper presents a complete study of threshold resonance states and resolvent expansions at a threshold for the Schrodinger operator on the discrete half-line N with a general boundary condition. A precise description of the expansion coefficients reveals their exact correspondence to the generalized eigenspaces, or the threshold types. The presentation of the paper is adapted from that of Ito-Jensen [Rev. Math. Phys. 27, 1550002 (2015)], implementing the expansion scheme of Jensen-Nenciu [Rev. Math. Phys. 13(6), 717-754 (2001) and Rev. Math. Phys. 16(5), 675-677 (2004)] in its full generality.

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©2017 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Mathematical Physics 58(5), 52101 and may be found at http://dx.doi.org/10.1063/1.4982957