# Generation of Schubert polynomial series by nanophotonics

## TL;DR

This paper demonstrates the first physical generation of Schubert polynomials using nanophotonics, specifically through optical near-field processes in a photochromic crystal, enabling reconfigurable complex pattern formation.

## Contribution

It introduces a novel method to generate Schubert polynomials via nanophotonics, bridging mathematical permutation theory with optical physical processes.

## Key findings

- Successfully generated Schubert matrices using optical near-field density mapping.
- Patterns can be reconfigured by adjusting photon detection sensitivity.
- First demonstration of Schubert polynomial generation through physical nanophotonic processes.

## Abstract

Generation of irregular time series based on physical processes is indispensable in computing and artificial intelligence. In this report, we propose and experimentally demonstrate the generation of Schubert polynomials, which is the foundation of versatile permutations in mathematics, via optical near-field processes introduced in a photochromic crystal of diarylethene, which optical near-field excitation on the surface of a photochromic single crystal yields a chain of local photoisomerization, forming a complex pattern on the opposite side of the crystal. The incoming photon travels through the nanostructured photochromic crystal, and the exit position of the photon exhibits a versatile pattern. We experimentally generated Schubert matrices, corresponding to Schubert polynomials, via optical near-field density mapping. The versatility and correlations of the generated patterns could be reconfigured in either a soft or hard manner by adjusting the photon detection sensitivity. This is the first study of Schubert polynomial generation by physical processes or nanophotonics, paving the way toward future nano-scale intelligence devices and systems.

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Source: https://tomesphere.com/paper/1907.05625