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

Ito, Kenichi  ,  Jensen, Arne

58 ( 5 )  , p.052101 , 2017-05 , AIP Publishing
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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