Spectral analysis near a dirac type crossing in a weak non-constant magnetic field

Autor: Radu Purice, Bernard Helffer, Horia D. Cornean

Publikováno v: 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

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 al

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https://vbn.aau.dk/da/publications/72d4b03c-91e3-4dec-b0aa-aaf927dd22b8

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

Autor: Radu Purice, Viorel Iftimie, Horia D. Cornean

Publikováno v: Cornean, D H, Iftimie, V & Purice, R 2019, ' Peierls' substitution via minimal coupling and magnetic pseudo-differential calculus ', Reviews in Mathematical Physics, vol. 31, no. 3, 1950008 . https://doi.org/10.1142/S0129055X19500089

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 ra

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https://vbn.aau.dk/da/publications/dec75b69-7455-45cb-8957-7c22cec6782b

A BEALS CRITERION FOR MAGNETIC PSEUDODIFFERENTIAL OPERATORS PROVED WITH MAGNETIC GABOR FRAMES

Autor: Horia D. Cornean, Bernard Helffer, Radu Purice

Publikováno v: Communications in Partial Differential Equations
Communications in Partial Differential Equations, Taylor & Francis, In press
Cornean, D H, Helffer, B & Purice, R 2018, ' A Beals criterion for magnetic pseudo-differential operators proved with magnetic Gabor frames ', Communications in Partial Differential Equations, vol. 43, no. 8, pp. 1196-1204 . https://doi.org/10.1080/03605302.2018.1499777

First, we give a new proof for the Beals commutator criterion for non-magnetic Weyl pseudo-differential operators based on classical Gabor tight frames. Second, by introducing a modified 'magnetic' Gabor tight frame, we naturally derive the magnetic

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https://hal.archives-ouvertes.fr/hal-01875406/document

Low lying spectral gaps induced by slowly varying magnetic fields

Autor: Bernard Helffer, Horia D. Cornean, Radu Purice

Publikováno v: Cornean, D H, Helffer, B & Purice, R 2017, ' Low lying spectral gaps induced by slowly varying magnetic fields ', Journal of Functional Analysis, vol. 273, no. 1, pp. 206-282 . https://doi.org/10.1016/j.jfa.2017.04.002
Journal of Functional Analysis
Journal of Functional Analysis, Elsevier, 2017, 273, pp.206--282

We consider a periodic Schr\"odinger operator in two dimensions perturbed by a weak magnetic field whose intensity slowly varies around a positive mean. We show in great generality that the bottom of the spectrum of the corresponding magnetic Schr\"o

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https://vbn.aau.dk/da/publications/f3c3bbde-c5db-4e65-9fcd-f36bd704f506

COHERENT STATES AND PURE STATE QUANTIZATION IN THE PRESENCE OF A VARIABLE MAGNETIC FIELD

Autor: Serge Richard, Radu Purice, Marius Mantoiu

Publikováno v: International Journal of Geometric Methods in Modern Physics. :187-202

We introduce magnetic coherent states for a particle in a variable magnetic field. They provide a pure state quantization of the phase space ℝ2N endowed with a magnetic symplectic form.

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https://doi.org/10.1142/s0219887811005087