Interior skin focusing and directional mirror transfer in a graded non-Hermitian Krawtchouk network
Abstract
Spatially graded nonreciprocity can move skin weight away from a boundary, but it does not generally preserve a real commensurate spectrum or analytically controlled dynamics. We study a finite open Krawtchouk network with oppositely graded directed hoppings. For a broad intermediate range of asymmetries, their local imaginary gauge field changes sign in the bulk, and its accumulated coordinate generates a positive diagonal similarity map whose normalized squared entries form a biased-binomial envelope. The same map converts the open chain into the spin-rotation generator 2gJx, so the focus and equally spaced spectrum follow from one grading. In this focusing regime, exact right, left, and biorthogonal eigenvectors show that the envelope width and participation number both scale as √N, identifying a subextensive interior focus. In the physical node basis, spin rotation produces perfect mirror inversion with direction-selective amplification and attenuation whose gains are mutually inverse. The directional Green functions share their poles, while their residues differ by the same similarity ratio. Closing the chain exposes a gauge-invariant imaginary flux, and either exact one-way limit yields an exceptional point of order N. Onsite disorder preserves the directional resolvent ratio, whereas independent hopping disorder breaks the clean analytic Krawtchouk map and degrades commensurability and transfer. The model therefore provides an exactly solvable finite-network framework linking localization geometry and eigenvector nonorthogonality to commensurate spectra and node-resolved directional response.
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BibTeX
@misc{liu2026interior,
title = {{Interior skin focusing and directional mirror transfer in a graded non-Hermitian Krawtchouk network}},
author = {Y. S. Liu and X. Z. Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.18800},
eprint = {2608.18800},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18800},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interior skin focusing and directional mirror transfer in a graded non-Hermitian Krawtchouk network
AU - Y. S. Liu
AU - X. Z. Zhang
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2608.18800
UR - https://arxiv.org/abs/2608.18800
AB - Spatially graded nonreciprocity can move skin weight away from a boundary, but it does not generally preserve a real commensurate spectrum or analytically controlled dynamics. We study a finite open Krawtchouk network with oppositely graded directed hoppings. For a broad intermediate range of asymmetries, their local imaginary gauge field changes sign in the bulk, and its accumulated coordinate generates a positive diagonal similarity map whose normalized squared entries form a biased-binomial envelope. The same map converts the open chain into the spin-rotation generator 2gJ_x, so the focus and equally spaced spectrum follow from one grading. In this focusing regime, exact right, left, and biorthogonal eigenvectors show that the envelope width and participation number both scale as √N, identifying a subextensive interior focus. In the physical node basis, spin rotation produces perfect mirror inversion with direction-selective amplification and attenuation whose gains are mutually inverse. The directional Green functions share their poles, while their residues differ by the same similarity ratio. Closing the chain exposes a gauge-invariant imaginary flux, and either exact one-way limit yields an exceptional point of order N. Onsite disorder preserves the directional resolvent ratio, whereas independent hopping disorder breaks the clean analytic Krawtchouk map and degrades commensurability and transfer. The model therefore provides an exactly solvable finite-network framework linking localization geometry and eigenvector nonorthogonality to commensurate spectra and node-resolved directional response.
ER -