Asymptotic anatomy of the Berry phase for scalar waves in two-dimensional periodic continua

doi:10.1098/rspa.2022.0110

CSpace > 应用数学研究所

	Asymptotic anatomy of the Berry phase for scalar waves in two-dimensional periodic continua
	Guzina, Bojan B.1; Oudghiri-Idrissi, Othman 1; Meng, Shixu2
	2022-06-29
发表期刊	PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
ISSN	1364-5021
卷号	478 期号:2262 页码:28
摘要	We deploy an asymptotic model for the interaction between nearby dispersion surfaces and respective eigenstates towards explicit evaluation of the Berry phase governed by the scalar wave equation in two-dimensional periodic media. The model, featuring a pair of coupled Dirac equations, entails a four-dimensional parametric space and endows the interacting Bloch eigenstates with an explicit gauge that caters for analytical integration in the wavenumber domain. Among the featured parameters, the one (s & ISIN;[0,12]) that synthesizes the phase information on the coupling term is shown to decide whether the Berry connection round the loop is singular (s=0) or analytic (s > 0). The analysis demonstrates that the Berry phase for two-dimensional lattices is pi-quantal and topological when s=0, equalling pi when the contour encloses a Dirac point and zero in all other situations (avoided crossings or line crossings). The analogous result is obtained, up to an O(s) residual, when s is an element of 0 and similarly for s is an element of 1/2. In the interior of the s-domain, we find that the Berry phase either approximately equals pi or is not quantal. Beyond shedding light on the anatomy of the Berry phase in periodic continua, the analysis carries a practical benefit as it permits a single-wavenumber evaluation of this geometrical phase quantity. The asymptotic estimates of the Berry phase are found to be in agreement with their numerical counterparts. For generality, we also include an application to a Dirac-like, three-energy-level system.
关键词	Berry phase asymptotic model scalar wave equation Berry phase computation
DOI	10.1098/rspa.2022.0110
收录类别	SCI
语种	英语
资助项目	endowed Shimizu Professorship
WOS研究方向	Science & Technology - Other Topics
WOS类目	Multidisciplinary Sciences
WOS记录号	WOS:000814685100002
出版者	ROYAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61242
专题	应用数学研究所
通讯作者	Guzina, Bojan B.
作者单位	1.Univ Minnesota, Dept Civil Environm & Geoengn, Minneapolis, MN 55405 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Guzina, Bojan B.,Oudghiri-Idrissi, Othman,Meng, Shixu. Asymptotic anatomy of the Berry phase for scalar waves in two-dimensional periodic continua[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES,2022,478(2262):28.
APA	Guzina, Bojan B.,Oudghiri-Idrissi, Othman,&Meng, Shixu.(2022).Asymptotic anatomy of the Berry phase for scalar waves in two-dimensional periodic continua.PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES,478(2262),28.
MLA	Guzina, Bojan B.,et al."Asymptotic anatomy of the Berry phase for scalar waves in two-dimensional periodic continua".PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 478.2262(2022):28.