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

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

2009-06-28

arxiv.org/abs/0906.5049v2

Phys. Rev. A. 81, 022107 (2010)

Physics

Quantum Physics

7 pages, 5 figures

Scientific paper

10.1103/PhysRevA.81.022107

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 $\pi$-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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