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Quantum Transport in Mesoscopic SystemsComplexity and Statistical Fluctuations. A Maximum Entropy Viewpoint$
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Pier A. Mello and Narendra Kumar

Print publication date: 2004

Print ISBN-13: 9780198525820

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525820.001.0001

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INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY II: SCATTERING INSIDE WAVEGUIDES AND CAVITIES

INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY II: SCATTERING INSIDE WAVEGUIDES AND CAVITIES

Chapter:
(p.120) 3 INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY II: SCATTERING INSIDE WAVEGUIDES AND CAVITIES
Source:
Quantum Transport in Mesoscopic Systems
Author(s):

Pier A. Mello

Narendra Kumar

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525820.003.0003

This chapter extends the potential scattering theory developed in Chapter 2 to a relatively advanced level with emphasis on quasi-one-dimensional (multi-channel) systems, the associated scattering and transfer matrices, and on how to combine them serially. Both the closed and the open channels are discussed. Scattering by a cavity with an arbitrary number of waveguides (the leads) attached to it is introduced. The Wigner R-matrix theory of two-dimensional scattering is treated in some detail with attention to boundary conditions. A non-trivial exactly soluble example for the two-channel scattering problem is also presented.

Keywords:   Lippmann-Schwinger equation, scattering matrix, transfer matrix, Wigner R-matrix, time-reversal invariance, open channel, close channel

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