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Trace formula for the magnetic Laplacian. / Kordyukov, Yu A.; Taimanov, I. A.

In: Russian Mathematical Surveys, Vol. 74, No. 2, 4, 01.01.2019, p. 325-361.

Research output: Contribution to journal › Article › peer-review

Harvard

Kordyukov, YA & Taimanov, IA 2019, 'Trace formula for the magnetic Laplacian', Russian Mathematical Surveys, vol. 74, no. 2, 4, pp. 325-361. https://doi.org/10.1070/RM9870

APA

Kordyukov, Y. A., & Taimanov, I. A. (2019). Trace formula for the magnetic Laplacian. Russian Mathematical Surveys, 74(2), 325-361. [4]. https://doi.org/10.1070/RM9870

Vancouver

Kordyukov YA, Taimanov IA. Trace formula for the magnetic Laplacian. Russian Mathematical Surveys. 2019 Jan 1;74(2):325-361. 4. doi: 10.1070/RM9870

Author

Kordyukov, Yu A. ; Taimanov, I. A. / Trace formula for the magnetic Laplacian. In: Russian Mathematical Surveys. 2019 ; Vol. 74, No. 2. pp. 325-361.

BibTeX

@article{71d2e624668840c4bb03428d07d5d1dd,
title = "Trace formula for the magnetic Laplacian",
abstract = "The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and the more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds, which reflects the dynamics of magnetic geodesic flows in terms of eigenvalues of a natural differential operator (the magnetic Laplacian) associated with the magnetic field. This paper gives a survey of basic notions and results related to the Guillemin-Uribe trace formula and provides concrete examples of its computation for two-dimensional constant curvature surfaces with constant magnetic fields and for the Katok example. Bibliography: 53 titles.",
keywords = "magnetic geodesics, magnetic Laplacian, trace formula, RIEMANN SURFACES, WAVE INVARIANTS, EIGEN-VALUE-PROBLEM, PERIODIC-ORBITS, CLOSED EXTREMALS, RESOLVENT, AUTOMORPHIC-FORMS, SPECTRUM, QUANTIZATION, OPERATORS",
author = "Kordyukov, {Yu A.} and Taimanov, {I. A.}",
year = "2019",
month = jan,
day = "1",
doi = "10.1070/RM9870",
language = "English",
volume = "74",
pages = "325--361",
journal = "Russian Mathematical Surveys",
issn = "0036-0279",
publisher = "IOP Publishing Ltd.",
number = "2",

}

RIS

TY - JOUR

T1 - Trace formula for the magnetic Laplacian

AU - Kordyukov, Yu A.

AU - Taimanov, I. A.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and the more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds, which reflects the dynamics of magnetic geodesic flows in terms of eigenvalues of a natural differential operator (the magnetic Laplacian) associated with the magnetic field. This paper gives a survey of basic notions and results related to the Guillemin-Uribe trace formula and provides concrete examples of its computation for two-dimensional constant curvature surfaces with constant magnetic fields and for the Katok example. Bibliography: 53 titles.

AB - The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and the more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds, which reflects the dynamics of magnetic geodesic flows in terms of eigenvalues of a natural differential operator (the magnetic Laplacian) associated with the magnetic field. This paper gives a survey of basic notions and results related to the Guillemin-Uribe trace formula and provides concrete examples of its computation for two-dimensional constant curvature surfaces with constant magnetic fields and for the Katok example. Bibliography: 53 titles.

KW - magnetic geodesics

KW - magnetic Laplacian

KW - trace formula

KW - RIEMANN SURFACES

KW - WAVE INVARIANTS

KW - EIGEN-VALUE-PROBLEM

KW - PERIODIC-ORBITS

KW - CLOSED EXTREMALS

KW - RESOLVENT

KW - AUTOMORPHIC-FORMS

KW - SPECTRUM

KW - QUANTIZATION

KW - OPERATORS

UR - http://www.scopus.com/inward/record.url?scp=85072728453&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=41693165

U2 - 10.1070/RM9870

DO - 10.1070/RM9870

M3 - Article

AN - SCOPUS:85072728453

VL - 74

SP - 325

EP - 361

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

SN - 0036-0279

IS - 2

M1 - 4

ER -

ID: 21741187