Quantum monodromy and semi-classical trace formula

被引：50

作者：

Sjöstrand, J ^{[1
]}

Zworski, M

机构：

[1] Ecole Polytech, Ctr Math, UMR 7460, CNRS, F-91128 Palaiseau, France

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2002年 / 81卷 / 01期

基金：

美国国家科学基金会;

关键词：

semi-classical; trace formula; monodromy;

D O I：

10.1016/S0021-7824(01)01230-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an h-pseudodifferential operator whose symbol has a closed Hamiltonian trajectory. There exists a Fourier integral operator which quantizes in a natural way the Poincare map. With the help of this monodromy operator, we give a trace formula which leads to a new proof of the trace formula of Duistermaat-Guillemin and Gutzwiller. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

引用

页码：1 / 33

页数：33

共 15 条

[1] [Anonymous], 2000, 1 SUMMER SCH ANAL MA
[2] A proof of the Gutzwiller semiclassical trace formula using coherent states decomposition
Combescure, M
Ralston, J
Robert, D
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 202 (02) : 463 - 480
[3] DAZORD P, 1977, J MATH PURE APPL, V56, P231
[4] Dimassi M., 1999, LONDON MATH SOC LECT, V269
[5] SPECTRUM OF POSITIVE ELLIPTIC OPERATORS AND PERIODIC BICHARACTERISTICS
DUISTERMAAT, JJ
GUILLEMIN, VW
[J]. INVENTIONES MATHEMATICAE, 1975, 29 (01) : 39 - 79
[6] Gutzwiller M. C., 1997, LECT NOTE PHYS, V485, P8
[7] HELFFER B, 1990, ANN I H POINCARE-PHY, V52, P303
[8] Helffer J., 1989, Mem. Soc. Math. Fr., V1, P1
[9] Hormander L., 1985, ANAL LINEAR PARTIAL
[10] Hormander L., 1985, ANAL LINEAR PARTIAL, VIV

← 1 2 →