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Quantum Multiple Scattering: Eigenmode Expansion and Its Applications to Proximity Resonance

Sheng Li·Eric J. Heller
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Abstract

We show that for a general system of N s-wave point scatterers, there are always N eigenmodes. These eigenmodes or eigenchannels play the same role as spherical harmonics for a spherically symmetric target--they give a phase shift only. In other words, the T matrix of the system is of rank N and the eigenmodes are eigenvectors corresponding to non-0 eigenvalues of the T matrix. The eigenmode expansion approach can give insight to the total scattering cross section; the position, width, and superradiant or subradiant nature of resonance peaks; the unsymmetric Fano lineshape of sharp proximity resonance peaks based on the high energy tail of a broad band; and other properties. Off-resonant eigenmodes for identical proximate scatterers are approximately angular momentum eigenstates.

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Sheng Li, Eric J. Heller. 2002-10-21. Quantum Multiple Scattering: Eigenmode Expansion and Its Applications to Proximity Resonance. https://arxiv.org/abs/physics/0112044

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