Spectral analysis near a dirac type crossing in a weak non-constant magnetic field
| Autor: | Radu Purice, Bernard Helffer, Horia D. Cornean |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
General Mathematics
Dirac (software) FOS: Physical sciences Dirac operator 01 natural sciences Mathematics - Spectral Theory symbols.namesake 0103 physical sciences FOS: Mathematics 0101 mathematics Spectral Theory (math.SP) Mathematical Physics Eigenvalues and eigenvectors Mathematics 35Q40 35S05 47G30 Series (mathematics) Applied Mathematics 010102 general mathematics Spectrum (functional analysis) Landau quantization Mathematical Physics (math-ph) Magnetic field Quantum electrodynamics symbols 010307 mathematical physics Constant (mathematics) |
| Zdroj: | CORNEAN, HORIA D, HELFFER, BERNARD & PURICE, RADU 2021, ' Spectral analysis near a dirac type crossing in a weak non-constant magnetic field ', Transactions of the American Mathematical Society, vol. 374, no. 10, pp. 7041-7104 . https://doi.org/10.1090/tran/8402 |
| DOI: | 10.1090/tran/8402 |
| Popis: | This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two $2d$ Bloch eigenvalues which have a conical crossing. It turns out that in the presence of an almost constant weak magnetic field, the spectrum near the crossing develops gaps which remind of the Landau levels of an effective mass-less magnetic Dirac operator. Comment: 51 pages, 2 figures. Will appear in Trans. A.M.S |
| Databáze: | OpenAIRE |
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