Review on Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle

Morin, Léo

doi:10.5802/cml.83

Confluentes Mathematici

2022

DOI: 10.5802/cml.83

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Review on Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle

Léo Morin¹

Abstract: Certains droits réservés. Cet article est mis à disposition selon les termes de la Licence Internationale d'Attribution Creative Commons BY-NC-ND 4.0 https://creativecommons.org/licenses/by-nc-nd/4.0/ Confluentes Mathematici est membre du Centre Mersenne pour l'édition scientifique ouverte http:// www.centre-mersenne.org/ e-

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Cited by 2 publications

References 22 publications

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Trace formula for the magnetic Laplacian at zero energy level

Kordyukov¹

2022

Uspekhi Mat. Nauk

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Работа посвящена формуле следа для магнитного лапласиана, ассоциированного с магнитной системой на компактном многообразии. Эта формула является естественным обобщением квазиклассической формулы следа Гуцвиллера и сводится к ней в случае, когда форма магнитного поля точна. Она несколько отличается от формулы следа Гийемина-Урибе, изучавшейся в предыдущей работе автора с И. А. Таймановым. Более того, в отличие от той работы основное внимание уделяется формуле следа на нулевом уровне энергии, являющемся критическим уровнем энергии. В работе дан обзор основных понятий и результатов, связанных с формулой следа на нулевом уровне энергии, описаны различные подходы к ее доказательству, приведены конкретные примеры ее вычисления. Кроме того, дан краткий обзор формулы следа Гуцвиллера для регулярных и критических уровней энергии. Библиография: 88 названий.

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Trace formula for the magnetic Laplacian at zero energy level

Kordyukov¹

2022

Uspekhi Mat. Nauk

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Trace formula for the magnetic Laplacian at zero energy level

Kordyukov

2022

Russian Math. Surveys

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The paper is devoted to the trace formula for the magnetic Laplacian associated with a magnetic system on a compact manifold. This formula is a natural generalization of Gutzwiller's semiclassical trace formula and reduces to it in the case when the magnetic field form is exact. It differs slightly from the Guillemin-Uribe trace formula considered in a previous paper of the author and Taimanov. Moreover, in contrast to that paper, the focus is on the trace formula at the zero energy level, which is a critical energy level. An overview of the main notions and results related to the trace formula at the zero energy level is presented, various approaches to its proof are described, and concrete examples of its computation are given. In addition, a brief review of Gutzwiller's trace formula for regular and critical energy levels is presented. Bibliography: 88 titles.

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Review on Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle

Cited by 2 publications

References 22 publications

Trace formula for the magnetic Laplacian at zero energy level

Trace formula for the magnetic Laplacian at zero energy level

Trace formula for the magnetic Laplacian at zero energy level

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