On the semiclassical analysis of the ground state energy of the Dirichlet Pauli operator III : magnetic fields that change sign
(2019) In Letters in Mathematical Physics 109(7). p.1533-1558- Abstract
We consider the semiclassical Dirichlet Pauli operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm–Kovařík–Portmann and Helffer–Sundqvist for the asymptotics of the ground state energy in the semiclassical limit when the magnetic field has constant sign. In this paper, we focus on the case when the magnetic field changes sign. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the semiclassical parameter tends to zero and give lower bounds and upper bounds for this decay rate. Concrete examples of magnetic fields changing sign on the unit disk are discussed. Various natural conjectures are disproved, and this... (More)
We consider the semiclassical Dirichlet Pauli operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm–Kovařík–Portmann and Helffer–Sundqvist for the asymptotics of the ground state energy in the semiclassical limit when the magnetic field has constant sign. In this paper, we focus on the case when the magnetic field changes sign. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the semiclassical parameter tends to zero and give lower bounds and upper bounds for this decay rate. Concrete examples of magnetic fields changing sign on the unit disk are discussed. Various natural conjectures are disproved, and this leaves the research of an optimal result in the general case still open.
(Less)
- author
- Helffer, Bernard ; Kovařík, Hynek and Sundqvist, Mikael P. LU
- organization
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Dirichlet, Flux effects, Pauli operator, Semiclassical
- in
- Letters in Mathematical Physics
- volume
- 109
- issue
- 7
- pages
- 1533 - 1558
- publisher
- Springer
- external identifiers
-
- scopus:85060144338
- ISSN
- 0377-9017
- DOI
- 10.1007/s11005-018-01153-9
- language
- English
- LU publication?
- yes
- id
- 8c2a8588-dd93-437d-9694-d91524564efc
- date added to LUP
- 2019-02-12 10:35:23
- date last changed
- 2022-04-10 06:02:01
@article{8c2a8588-dd93-437d-9694-d91524564efc,
abstract = {{<p>We consider the semiclassical Dirichlet Pauli operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm–Kovařík–Portmann and Helffer–Sundqvist for the asymptotics of the ground state energy in the semiclassical limit when the magnetic field has constant sign. In this paper, we focus on the case when the magnetic field changes sign. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the semiclassical parameter tends to zero and give lower bounds and upper bounds for this decay rate. Concrete examples of magnetic fields changing sign on the unit disk are discussed. Various natural conjectures are disproved, and this leaves the research of an optimal result in the general case still open.</p>}},
author = {{Helffer, Bernard and Kovařík, Hynek and Sundqvist, Mikael P.}},
issn = {{0377-9017}},
keywords = {{Dirichlet; Flux effects; Pauli operator; Semiclassical}},
language = {{eng}},
number = {{7}},
pages = {{1533--1558}},
publisher = {{Springer}},
series = {{Letters in Mathematical Physics}},
title = {{On the semiclassical analysis of the ground state energy of the Dirichlet Pauli operator III : magnetic fields that change sign}},
url = {{http://dx.doi.org/10.1007/s11005-018-01153-9}},
doi = {{10.1007/s11005-018-01153-9}},
volume = {{109}},
year = {{2019}},
}