Abstract
A mathematical model for a simple microscheme is constructed on the basis of the scattering theory for a pair of different self-adjoint extensions of the same symmetric ordinary differential operator on a one-dimensional manifold, which consist of a finite number of semiinfinite straight outer lines attached to a “black box” in a form of a flat connected graph. An explicit expression for the scattering is given under a continuity condition at the graph vertices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adamyan, V. M.; Pavlov, B. S.: Null-range potentials and M. G. Krein’s formula of generalized resolvents (in Russian), Studies on linear operators of functions. XV. Research notes of scientific seminars of the LBMI, 1986, v. 149, pp. 7–23.
Exner, P.; Šeba, P.: A new type of quantum interference transistor, Phys. Lett. A 129:8,9 (1988), 477–480.
Reed, M.; Simon, B.: Methods of modern mathematical physics. III: Scattering theory, Academic Press, New York — San Francisco — London, 1979.
Krein, M. G.: On the resolvents of a Hermitian operator with the defect indices (m, m) (in Russian), Dokl Acad. Nauk SSSR 52:8 (1946), 657–660.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Basel AG
About this chapter
Cite this chapter
Adamyan, V. (1992). Scattering Matrices for Micro Schemes. In: Ando, T., Gohberg, I. (eds) Operator Theory and Complex Analysis. Operator Theory: Advances and Applications, vol 59. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8606-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8606-2_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9699-3
Online ISBN: 978-3-0348-8606-2
eBook Packages: Springer Book Archive