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arXiv · 2102.02737

Insight of the Green's function as a defect state in a boundary value problem

Jose D. H. Rivero·Li Ge
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Abstract

A new perspective of the Green's function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green's function can be perceived as a defect state in the presence of a $\delta$-function potential, the height of which depends on the Green's function itself. This approach is illustrated in one-dimensional and two-dimensional Helmholtz equation problems, with an emphasis on systems that are open and have a non-Hermitian potential. We then draw an analogy between the Green's function obtained this way and a chiral edge state circumventing a defect in a topological lattice, which shines light on the local minimum of the Green's function at the source position.

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Jose D. H. Rivero, Li Ge. 2021-02-04. Insight of the Green's function as a defect state in a boundary value problem. https://doi.org/10.1103/physrevb.103.195142

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