Exact formulas of the end-to-end Green's functions in non-Hermitian systems

• URL: http://arxiv.org/abs/2109.03045v3
• Date: Wed, 19 Jan 2022 03:45:29 GMT
• Title: Exact formulas of the end-to-end Green's functions in non-Hermitian systems
• Authors: Haoshu Li, Shaolong Wan
• Abstract summary: Green's function in non-Hermitian systems can be capable of directional amplification. We derive exact formulas for the end-to-end Green's functions of single-band systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Green's function in non-Hermitian systems has recently been revealed to be capable of directional amplification in some cases. The exact formulas for end-to-end Green's functions are significantly important for studies of both non-Hermitian systems and their applications. In this work, based on the Widom's formula, we derive exact formulas for the end-to-end Green's functions of single-band systems which depend on the roots of a simple algebraic equation. These exact formulas allow direct and accurate comparisons between theoretical results and experimentally measured quantities. In addition, we verify the prior established integral formula in the bulk region to agree with the result in our framework. We also find that the speed at which the Green's functions in the bulk region approach the prior established integral formula is not slower than an exponential decay as the system size increases. The correspondence between the signal amplification and the non-Hermitian skin effect is confirmed.

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