Flux and symmetry effects on quantum tunneling
(2024) In Mathematische Annalen- Abstract
Motivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitian matrix. We illustrate this framework by three applications, firstly the electro-magnetic Laplacian with constant magnetic field and three equidistant potential wells, secondly a pure constant magnetic field and Neumann boundary condition in a smoothed triangle, and thirdly a magnetic step where the discontinuity line is a smoothed triangle. Flux effects are visible in the three aforementioned settings through the occurrence of eigenvalue crossings. Moreover, in the electro-magnetic Laplacian setting with double well radial potential, we rule out an... (More)
Motivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitian matrix. We illustrate this framework by three applications, firstly the electro-magnetic Laplacian with constant magnetic field and three equidistant potential wells, secondly a pure constant magnetic field and Neumann boundary condition in a smoothed triangle, and thirdly a magnetic step where the discontinuity line is a smoothed triangle. Flux effects are visible in the three aforementioned settings through the occurrence of eigenvalue crossings. Moreover, in the electro-magnetic Laplacian setting with double well radial potential, we rule out an artificial condition on the distance of the wells and extend the range of validity for the tunneling approximation recently established in Fefferman et al. (SIAM J Math Anal 54: 1105–1130, 2022), Helffer & Kachmar (Pure Appl Anal, 2024), thereby settling the problem of electro-magnetic tunneling under constant magnetic field and a sum of translated radial electric potentials.
(Less)
- author
- Helffer, Bernard ; Kachmar, Ayman LU and Sundqvist, Mikael Persson LU
- organization
- publishing date
- 2024
- type
- Contribution to journal
- publication status
- epub
- subject
- keywords
- 81U26
- in
- Mathematische Annalen
- publisher
- Springer
- external identifiers
-
- scopus:85192055526
- ISSN
- 0025-5831
- DOI
- 10.1007/s00208-024-02874-0
- language
- English
- LU publication?
- yes
- id
- 2d33c3a1-5b58-4005-b741-5a301dc6ea91
- date added to LUP
- 2024-05-21 15:27:32
- date last changed
- 2024-05-21 15:28:45
@article{2d33c3a1-5b58-4005-b741-5a301dc6ea91,
abstract = {{<p>Motivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitian matrix. We illustrate this framework by three applications, firstly the electro-magnetic Laplacian with constant magnetic field and three equidistant potential wells, secondly a pure constant magnetic field and Neumann boundary condition in a smoothed triangle, and thirdly a magnetic step where the discontinuity line is a smoothed triangle. Flux effects are visible in the three aforementioned settings through the occurrence of eigenvalue crossings. Moreover, in the electro-magnetic Laplacian setting with double well radial potential, we rule out an artificial condition on the distance of the wells and extend the range of validity for the tunneling approximation recently established in Fefferman et al. (SIAM J Math Anal 54: 1105–1130, 2022), Helffer & Kachmar (Pure Appl Anal, 2024), thereby settling the problem of electro-magnetic tunneling under constant magnetic field and a sum of translated radial electric potentials.</p>}},
author = {{Helffer, Bernard and Kachmar, Ayman and Sundqvist, Mikael Persson}},
issn = {{0025-5831}},
keywords = {{81U26}},
language = {{eng}},
publisher = {{Springer}},
series = {{Mathematische Annalen}},
title = {{Flux and symmetry effects on quantum tunneling}},
url = {{http://dx.doi.org/10.1007/s00208-024-02874-0}},
doi = {{10.1007/s00208-024-02874-0}},
year = {{2024}},
}