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量子模拟是研究和理解量子世界中奇异物理现象的重要手段. 近年来, 人们发现除了量子平台, 经典系统 (如光子晶体、声子晶体和机械振子等) 也能通过类比薛定谔方程的方式模拟量子模型. 其中, 经典电路因具有成本低廉、技术成熟和易于扩展等特点, 成为一个新兴的模拟平台, 并成功模拟了许多重要的量子现象. 与此同时, 非厄米物理突破了传统量子力学中系统哈密顿量的厄米性, 为人们理解量子系统, 尤其是开放量子系统中的物理, 提供了一种新的视角. 非厄米系统由于展现出不同于厄米系统的新奇现象, 在物理学的多个领域中成为新兴的研究对象. 然而, 许多非厄米现象所要求的奇异构型在量子平台上实现的技术门槛相对较高, 例如非厄米趋肤效应通常需要系统具备非互易的格点间跃迁. 因此, 利用操控灵活的经典电路模拟非厄米物理成为一种自然的选择. 本文旨在通过简要介绍非厄米物理的相关知识 (包括数学基础和新奇现象) 以及经典电路的模拟理论 (包括对格点模型的映射理论、非厄米的引入和物理量的测量等), 概述当前经典电路模拟非厄米格点模型的实验进展, 为相关研究工作提供参考, 以推动该领域的进一步发展.
Quantum simulation serves as a significant tool for studying and understanding novel phenomena in the quantum world. In recent years, it has be realized that apart from quantum platforms, classical systems like photonic crystals, phononic crystals, and mechanical oscillators can also be used to simulate quantum models by analogizing the Schrödinger equation. Among these systems, electrical circuits have emerged as a promising simulation platform owing to their low cost, technological maturity, and ease of scalability, successfully simulating numerous important quantum phenomena. Meanwhile, non-Hermitian physics breaks the Hermiticity of systems’ Hamiltonians in traditional quantum mechanics, providing a fresh perspective for understanding the physics of quantum systems, particularly open quantum systems. Non-Hermitian systems, owing to their manifestation of unique phenomena absent in Hermitian systems, have become emerging research subjects in various fields of physics. However, many non-Hermitian phenomena require specialized configurations that pose relatively high technical thresholds on quantum platforms. For instance, the non-Hermitian skin effect typically requires systems to possess non-reciprocal hopping between lattice sites. Therefore, utilizing flexible electrical circuits to simulate non-Hermitian physics becomes a natural choice. This paper provides a short review of the current experimental progress in simulating non-Hermitian lattice models by using electrical circuits. It offers a brief introduction to the relevant knowledge of non-Hermitian physics, including mathematical concepts and novel phenomena, as well as the simulation theory of electrical circuits, including the mapping theory of the lattice models, the introduction of non-Hermiticity, and the measurement of physical quantities. The aim is to provide readers with a reference for better understanding or engagement in related researches, thus promoting further development in this field. -
Keywords:
- non-Hermitian physics/
- electrical circuit simulation/
- PT symmetry breaking/
- non-Hermitian skin effect/
- non-Hermitian topology
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