虚数エネルギーと運動量の理論(The Theory of Imaginary Energy and Momentum)

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2024-02-27 韓国基礎科学研究院(IBS)

ノイターのセミナー定理では、物理システムの連続対称性と保存則の関連が述べられている。非エルミート物理学では、開放系におけるエネルギーや運動量の保存が解決される。また、一般化されたブリルアンゾーンの理論では、複素運動量空間におけるトポロジカル位相転移が議論され、開放系における新しいトポロジカル状態の可能性が示唆されている。

<関連情報>

一般化ブリルアン領域のトポロジカル相転移 Topological phase transitions of generalized Brillouin zone

Sonu Verma & Moon Jip Park
Communications Physics  Published:09 January 2024
DOI:https://doi.org/10.1038/s42005-024-01519-7

虚数エネルギーと運動量の理論(The Theory of Imaginary Energy and Momentum)

Abstract

It has been known that the bulk-boundary correspondence (BBC) of the non-Hermitian skin effect is characterized by the topology of the complex eigenvalue spectra, while the topology of the wave function gives rise to Hermitian BBC with conventional boundary modes. In this work, we go beyond the known description of the non-Hermitian topological phase and find a different type of BBC that appears in generalized boundary conditions. The generalized Brillouin zone (GBZ) possesses non-trivial topological structures in the intermediate boundary condition between open and periodic boundary conditions. Unlike the conventional BBC, the topological phase transition is characterized by the generalized momentum touching of GBZ, which manifests as exceptional points. As a realization of our proposal, we suggest the non-reciprocal Kuramoto oscillator lattice, where phase slips accompany exceptional points as a signature of such topological phase transition. Our work establishes an understanding of non-Hermitian topological matter by complementing the non-Hermitian BBC as a general foundation of the non-Hermitian topological systems.

1701物理及び化学
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