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Modern Analysis and Applications pp 3–26Cite as

Modified Krein Formula and Analytic Perturbation Procedure for Scattering on Arbitrary Junction

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 190))

Abstract

The single-electron transport through a junction of quantum network is modeled as a specific scattering problem for the Schrödinger operator on the system of semi-infinite cylindrical domains (quantum wires) short-circuited by a compact domain (quantum well or dot). For calculation of the one-body scattering parameters of any junction having form of a compact domain with piece-wise smooth boundary and attached thin wires a semi-analytic perturbation procedure based on a specially selected intrinsic large parameter is suggested. The approximate scattering matrix of a thin junction obtained in this way is the scattering matrix of the corresponding solvable model.

This work was partially supported by the US Civilian Research and Development Foundation (CRDF) and the Government of Ukraine under Grant UM2-2811-OD06.

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Author information

Authors and Affiliations

  1. Department of Theorertical Physics, Odessa I.I. Mechnikov National University, 65082, Odessa, Ukraine

    V. Adamyan

  2. NZ Institute for Advanced Studies, Institute of Information and Mathematical Sciences, Massey University, Albany Campus, Private Bag 102-904, North Shore Mail Centre, Auckland, New Zealand

    B. Pavlov

  3. V. Fock Institute for Physics, St. Petersbourg University, 198904, St. Petersburg, Russian Federation

    A. Yafyasov

Authors
  1. V. Adamyan
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  2. B. Pavlov
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  3. A. Yafyasov
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Vadim M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Israel Gohberg

  3. Institute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska st., 01601, Kyiv-4, Ukraine

    Anatoly Kochubei , Yurij Berezansky , Myroslav Gorbachuk  & Valentyna Gorbachuk , ,  & 

  4. Department of Mathematical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Gennadiy Popov

  5. Institute of Analysis and Scientific Computing, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Heinz Langer

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To the memory of Mark Grigorjevich Krein

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Adamyan, V., Pavlov, B., Yafyasov, A. (2009). Modified Krein Formula and Analytic Perturbation Procedure for Scattering on Arbitrary Junction. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 190. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9919-1_3

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