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

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 $\pi$-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.

7 pages, 5 figures

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• Sudden death of particle-pair Bloch oscillation and unidirectional propagation in a one-dimensional driven optical lattice
• Perfect coherent shift of bound pairs in strongly correlated systems
• Fast transfer and efficient coherent separation of bound cluster in the extended Hubbard model
• Exact evaluation of the causal spectrum and localization properties of electronic states on a scale-free network
• Equivalent spin-orbit interaction in two-polariton Jaynes-Cummings-Hubbard model