Tunneling estimates for magnetic Schrödinger operators
type: Item
instance of: scholarly article
title: Tunneling estimates for magnetic Schrödinger operators
zbMATH Open document ID: 0922.35105
author: S. Nakamura
published in: Communications in Mathematical Physics
publication date: 1999-03-30T00:00:00Z
review text: The author studies the semiclassical exponential decay of the eigenfunctions of a bidimensional magnetic Schrödinger operator. The magnetic field \(B\) is assumed to be constant, and the electric potential \(V\) is supposed to form a simple well, and to be analytic with respect to rotations. Then, by conjugating the operator with a convenient exponential weight, the author finds a lower bound for the rate of decay of the eigenfunctions, which involves explicitly \(B\). In particular, this bound increases with \(| B|\), and it becomes optimal when \(V\) is assumed to be radial. An application to tunneling is also given when \(V\) is a smooth symmetric double well.
reviewed by: André Martinez
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35Q40
zbMATH DE Number: 1271627
zbMATH Keywords: phase space tunneling
zbMATH Keywords: semiclassical exponential decay
MaRDI profile type: Publication
full work available at URL: s002200050520
OpenAlex ID: W2037496189
DOI: 10.1007/S002200050520
description: scientific article; zbMATH DE number 1271627