Peierls’ substitution via minimal coupling and magnetic pseudo-differential calculus

2019 ◽  
Vol 31 (03) ◽  
pp. 1950008
Author(s):  
Horia D. Cornean ◽  
Viorel Iftimie ◽  
Radu Purice
Keyword(s):  
Magnetic Field ◽  
Differential Calculus ◽  
Spectral Band ◽  
Spatial Decay ◽  
Minimal Coupling ◽  
Field Perturbation ◽  
Wannier Functions ◽  
Weak Magnetic Fields ◽  
The Magnetic Field ◽  
Magnetic Field Perturbation

We revisit the celebrated Peierls–Onsager substitution for weak magnetic fields with no spatial decay conditions. We assume that the non-magnetic [Formula: see text]-periodic Hamiltonian has an isolated spectral band whose Riesz projection has a range which admits a basis generated by [Formula: see text] exponentially localized composite Wannier functions. Then we show that the effective magnetic band Hamiltonian is unitarily equivalent to a Hofstadter-like magnetic matrix living in [Formula: see text]. In addition, if the magnetic field perturbation is slowly variable in space, then the perturbed spectral island is close (in the Hausdorff distance) to the spectrum of a Weyl quantized minimally coupled symbol. This symbol only depends on [Formula: see text] and is [Formula: see text]-periodic; if [Formula: see text], the symbol equals the Bloch eigenvalue itself. In particular, this rigorously formulates a result from 1951 by J. M. Luttinger.

scholarly journals Discovery of weak magnetic fields in four DZ white dwarfs in the local 20 pc volume

2019 ◽  
Vol 630 ◽  
pp. A65 ◽  
Author(s):  
S. Bagnulo ◽  
J. D. Landstreet
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
White Dwarfs ◽  
Field Measurements ◽  
Weak Magnetic Fields ◽  
Polluted Atmosphere ◽  
Highly Sensitive ◽  
Cool White Dwarfs ◽  
The Magnetic Field ◽  
Made In

We report the discovery of weak magnetic fields in three white dwarfs within the local 20 pc volume (WD 0816−310, WD 1009−184, and WD 1532+129), and we confirm the magnetic nature of a fourth star (WD 2138−332) in which we had previously detected a field at a 3σ level. The spectra of all these white dwarfs are characterised by the presence of metal lines and lack of H and He lines, that is, they belong to the spectral class DZ. The polarisation signal of the Ca II H+K lines of WD 1009−184 is particularly spectacular, with an amplitude of 20% that is due to the presence of a magnetic field with an average line-of-sight component of 40 kG. We have thus established that at least 40% of the known DZ white dwarfs with an He-rich atmosphere contained in the 20 pc volume have a magnetic field, while further observations are needed to establish whether the remaining DZ white dwarfs in the same volume are magnetic or not. Metal lines in the spectra of DZ white dwarfs are thought to have originated by accretion from rocky debris, and it might be argued that a link exists between metal accretion and higher occurrence of magnetism. However, we are not able to distinguish whether the magnetic field and the presence of a polluted atmosphere have a common origin, or if it is the presence of metal lines that allows us to detect a higher frequency of magnetic fields in cool white dwarfs, which would otherwise have featureless spectra. We argue that the new highly sensitive longitudinal field measurements that we have made in recent years are consistent with the idea that the magnetic field appears more frequently in older than in younger white dwarfs.

scholarly journals Cosmic ray driven dynamo in barred and ringed galaxies

2010 ◽  
Vol 6 (S274) ◽  
pp. 398-400
Author(s):  
K. Kulpa-Dybeł ◽  
K. Otmianowska-Mazur ◽  
B. Kulesza-Żydzik ◽  
G. Kowal ◽  
D. Wóltański ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Radio Emission ◽  
High Frequency ◽  
Galactic Disk ◽  
Cosmic Ray ◽  
Field Configuration ◽  
Magnetic Field Configuration ◽  
Global Evolution ◽  
Weak Magnetic Fields ◽  
The Magnetic Field

AbstractWe study the global evolution of the magnetic field and interstellar medium (ISM) of the barred and ringed galaxies in the presence of non-axisymmetric components of the potential, i.e. the bar and/or the oval perturbations. The magnetohydrodynamical dynamo is driven by cosmic rays (CR), which are continuously supplied to the disk by supernova (SN) remnants. Additionally, weak, dipolar and randomly oriented magnetic field is injected to the galactic disk during SN explosions. To compare our results directly with the observed properties of galaxies we construct realistic maps of high-frequency polarized radio emission. The main result is that CR driven dynamo can amplify weak magnetic fields up to few μG within few Gyr in barred and ringed galaxies. What is more, the modelled magnetic field configuration resembles maps of the polarized intensity observed in barred and ringed galaxies.

scholarly journals Evolution of quasi-bound states in the circular n–p junction of bilayer graphene under magnetic field

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Haijiao Ji ◽  
Yueting Pan ◽  
Haiwen Liu
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Bound States ◽  
Local Density ◽  
Energy Levels ◽  
Bilayer Graphene ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Weak Magnetic Fields ◽  
The Magnetic Field

Abstract Electron in gapless bilayer graphene can form quasi-bound states when a circular symmetric potential is created in bilayer graphene. These quasi-bound states can be adjusted by tuning the radius and strength of the potential barrier. We investigate the evolution of quasi-bound states spectra in the circular n–p junction of bilayer graphene under the magnetic field numerically. The energy levels of opposite angular momentum split and the splitting increases with the magnetic field. Moreover, weak magnetic fields can slightly shift the energy levels of quasi-bound states. While strong magnetic fields induce additional resonances in the local density states, which originates from Landau levels. We demonstrate that these numerical results are consistent with the semiclassical analysis based on Wentzel–Kramers–Brillouin approximation. Our results can be verified experimentally via scanning tunneling microscopy measurements.

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