On Generalized WKB Expansion of Monodromy Generating Function

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-06-21 DOI:10.3842/SIGMA.2023.026

R. Klimov

引用次数: 0

Abstract

We study symplectic properties of the monodromy map of the Schrödinger equation on a Riemann surface with a meromorphic potential having second-order poles. At first, we discuss the conditions for the base projective connection, which induces its own set of Darboux homological coordinates, to imply the Goldman Poisson structure on the character variety. Using this result, we extend the paper [Theoret. and Math. Phys. 206 (2021), 258-295, arXiv:1910.07140], by performing generalized WKB expansion of the generating function of monodromy symplectomorphism (the Yang-Yang function) and computing its first three terms.

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关于单调生成函数的广义WKB展开

我们研究了具有二阶极点的亚纯势的Riemann曲面上Schrödinger方程的单调映射的辛性质。首先，我们讨论了基投影连接的条件，它导出了自己的一组Darboux同源坐标，从而在特征变化上暗示了Goldman-Poisson结构。利用这一结果，我们对论文[定理和数学物理.206（2021），258-295，arXiv:1910.07140]进行了推广，对单调亚纯的生成函数（杨函数）进行了广义WKB展开，并计算了它的前三项。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.