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On the semiclassical analysis of the ground state energy of the Dirichlet Pauli operator III : magnetic fields that change sign

Helffer, Bernard; Kovařík, Hynek and Sundqvist, Mikael P. LU (2019) In Letters in Mathematical Physics
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.

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author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Dirichlet, Flux effects, Pauli operator, Semiclassical
in
Letters in Mathematical Physics
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
2019-02-20 11:50:37
@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},
  keyword      = {Dirichlet,Flux effects,Pauli operator,Semiclassical},
  language     = {eng},
  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},
  year         = {2019},
}