Characterizing exceptional points using neural networks

IF 1.8 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

EPL Pub Date : 2023-11-14 DOI:10.1209/0295-5075/ad0c6f

Md Afsar Reja, Awadhesh Narayan

引用次数: 1

Abstract

Abstract One of the key features of non-Hermitian systems is the occurrence of exceptional points (EPs), spectral degeneracies where the eigenvalues and eigenvectors merge. In this work, we propose applying neural networks to characterize EPs by introducing a new feature -- summed phase rigidity (SPR). We consider different models with varying degrees of complexity to illustrate our approach, and show how to predict EPs for two-site and four-site gain and loss models. Further, we demonstrate an accurate EP prediction in the paradigmatic Hatano-Nelson model for a variable number of sites. Remarkably, we show how SPR enables a prediction of EPs of orders completely unseen by the training data. Our method can be useful to characterize EPs in an automated manner using machine learning approaches.

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用神经网络表征异常点

摘要非厄米系统的一个重要特征是在特征值和特征向量合并处存在异常点(EPs)，即谱简并。在这项工作中，我们建议应用神经网络通过引入一个新的特征-总相刚度(SPR)来表征EPs。我们考虑了不同复杂程度的不同模型来说明我们的方法，并展示了如何预测两位点和四位点损益模型的EPs。此外，我们证明了典型的Hatano-Nelson模型对可变站点数量的EP预测是准确的。值得注意的是，我们展示了SPR如何能够预测训练数据完全看不到的订单EPs。我们的方法可以用于使用机器学习方法以自动化的方式表征EPs。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

EPL 物理-物理：综合

CiteScore

3.30

自引率

5.60%

发文量

332

审稿时长

1.9 months

期刊介绍： General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology. Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate). EPL also publishes Comments on Letters previously published in the Journal.