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A Solvable Model for Scattering on a Junction and a Modified Analytic Perturbation Procedure

  • B. Pavlov
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Part of the Operator Theory: Advances and Applications book series (OT, volume 197)

Abstract

We consider a one-body spin-less electron spectral problem for a resonance scattering system constructed of a quantum well weakly connected to a noncompact exterior reservoir, where the electron is free. The simplest kind of the resonance scattering system is a quantum network, with the reservoir composed of few disjoint cylindrical quantum wires, and the Schrödinger equation on the network, with the real bounded potential on the wells and constant potential on the wires. We propose a Dirichlet-to-Neumann-based analysis to reveal the resonance nature of conductance across the star-shaped element of the network (a junction), derive an approximate formula for the scattering matrix of the junction, construct a fitted zero-range solvable model of the junction and interpret a phenomenological parameter arising in Datta- Das Sarma boundary condition, see [14], for T-junctions. We also propose using of the fitted zero-range solvable model as the first step in a modified analytic perturbation procedure of calculation of the corresponding scattering matrix.

Mathematics Subject Classification (2000)

Primary 47A40 47A48 47A55 Secondary 47N50 47N70 35Q40 

Keywords

Junction Fitted zero-range model Dirichlet-to-Neumann map 

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© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • B. Pavlov
    • 1
  1. 1.V.A. Fock Institute for Physics of St.-Petersburg UniversityPetrodvoretsRussia

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