Non-Real Eigenvalues for PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{PT}}}$$\end{document}-Symmetric Double Wells

被引：0

作者：

Amina Benbernou

Naima Boussekkine

Nawal Mecherout

Thierry Ramond

Johannes Sjöstrand

机构：

[1] Université de Mostaganem,Faculté des Sciences Exactes et Informatique

[2] Université Paris-Sud,Laboratoire de Mathématiques d’Orsay

[3] CNRS,Institut de Mathématiques de Bourgogne (UMR 5584 du CNRS)

[4] Université Paris-Saclay,undefined

[5] Université de Bourgogne,undefined

来源：

Letters in Mathematical Physics | 2016年 / 106卷 / 12期

关键词：

PT-symmetry; Schrödinger operator; double well; eigenvalues; 35P20; 35Q40; 81Q12; 81Q20;

D O I：

10.1007/s11005-016-0852-8

中图分类号：

学科分类号：

摘要：

We study small, PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{PT}}}$$\end{document}-symmetric perturbations of self-adjoint double-well Schrödinger operators in dimension n≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n\ge 1}$$\end{document}. We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the perturbation gets stronger.

引用

页码：1817 / 1835

页数：18

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