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 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
 epub
 subject
 keywords
 Dirichlet, Flux effects, Pauli operator, Semiclassical
 in
 Letters in Mathematical Physics
 publisher
 Springer
 external identifiers

 scopus:85060144338
 ISSN
 03779017
 DOI
 10.1007/s11005018011539
 language
 English
 LU publication?
 yes
 id
 8c2a8588dd93437d9694d91524564efc
 date added to LUP
 20190212 10:35:23
 date last changed
 20190220 11:50:37
@article{8c2a8588dd93437d9694d91524564efc, 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 = {03779017}, 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/s11005018011539}, year = {2019}, }