{"title":"Spectral properties of the linearized Balescu‐Lenard operator","authors":"A. H. Merchant, R. Liboff","doi":"10.1063/1.1666162","DOIUrl":null,"url":null,"abstract":"The spectrum of the linearized Balescu‐Lenard operator is studied in detail. It is found to be continuous, to range from zero to minus infinity, and to have no point spectrum. Analytic expressions are obtained for the l = 1 spherical harmonic eigenfunctions in the velocity domain ≳2.5, where x is microscopic speed, nondimensionalized through the thermal speed. Sketches showing the typical behavior for all x of this; l‐mode eigenfunction are also given.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"1973-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics Analysis Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/1.1666162","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 7
Abstract
The spectrum of the linearized Balescu‐Lenard operator is studied in detail. It is found to be continuous, to range from zero to minus infinity, and to have no point spectrum. Analytic expressions are obtained for the l = 1 spherical harmonic eigenfunctions in the velocity domain ≳2.5, where x is microscopic speed, nondimensionalized through the thermal speed. Sketches showing the typical behavior for all x of this; l‐mode eigenfunction are also given.
期刊介绍：
Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects:
mathematical problems of modern physics;
complex analysis and its applications;
asymptotic problems of differential equations;
spectral theory including inverse problems and their applications;
geometry in large and differential geometry;
functional analysis, theory of representations, and operator algebras including ergodic theory.
The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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