{"title":"非线性边缘模式玻色化中的贝里相位","authors":"Mathieu Beauvillain, Blagoje Oblak, Marios Petropoulos","doi":"arxiv-2408.03991","DOIUrl":null,"url":null,"abstract":"We consider chiral, generally nonlinear density waves in one dimension,\nmodelling the bosonized edge modes of a two-dimensional fermionic topological\ninsulator. Using the coincidence between bosonization and Lie-Poisson dynamics\non an affine U(1) group, we show that wave profiles which are periodic in time\nproduce Berry phases accumulated by the underlying fermionic field. These\nphases can be evaluated in closed form for any Hamiltonian, and they serve as a\ndiagnostic of nonlinearity. As an explicit example, we discuss the Korteweg-de\nVries equation, viewed as a model of nonlinear quantum Hall edge modes.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":"95 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Berry Phases in the Bosonization of Nonlinear Edge Modes\",\"authors\":\"Mathieu Beauvillain, Blagoje Oblak, Marios Petropoulos\",\"doi\":\"arxiv-2408.03991\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider chiral, generally nonlinear density waves in one dimension,\\nmodelling the bosonized edge modes of a two-dimensional fermionic topological\\ninsulator. Using the coincidence between bosonization and Lie-Poisson dynamics\\non an affine U(1) group, we show that wave profiles which are periodic in time\\nproduce Berry phases accumulated by the underlying fermionic field. These\\nphases can be evaluated in closed form for any Hamiltonian, and they serve as a\\ndiagnostic of nonlinearity. As an explicit example, we discuss the Korteweg-de\\nVries equation, viewed as a model of nonlinear quantum Hall edge modes.\",\"PeriodicalId\":501155,\"journal\":{\"name\":\"arXiv - MATH - Symplectic Geometry\",\"volume\":\"95 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Symplectic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.03991\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Symplectic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03991","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Berry Phases in the Bosonization of Nonlinear Edge Modes
We consider chiral, generally nonlinear density waves in one dimension,
modelling the bosonized edge modes of a two-dimensional fermionic topological
insulator. Using the coincidence between bosonization and Lie-Poisson dynamics
on an affine U(1) group, we show that wave profiles which are periodic in time
produce Berry phases accumulated by the underlying fermionic field. These
phases can be evaluated in closed form for any Hamiltonian, and they serve as a
diagnostic of nonlinearity. As an explicit example, we discuss the Korteweg-de
Vries equation, viewed as a model of nonlinear quantum Hall edge modes.
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