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arXiv · 0906.5049

Rigorous results for tight-binding networks: particle trapping and scattering

L. Jin·Z. Song
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Abstract

We investigate the particle trapping and scattering properties in a tight-binding network which consists of several subgraphs. The particle trapping condition is proved under which particles can be trapped in a subgraph without leaking. Based on exact solutions for the configuration of a $π$-shaped lattice, it is argued that the bound states in a specified subgraph are of two types, resonant and evanescent. It is also shown that, when such a subgraph is embedded in a one-dimensional chain as the waveguide, an incident wave experiences total reflection if its energy matches the resonant bound state energy.

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L. Jin, Z. Song. 2009-11-04. Rigorous results for tight-binding networks: particle trapping and scattering. https://doi.org/10.1103/physreva.81.022107

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