2D random magnetic Laplacian with white noise magnetic field

2021/01/13 by Morin, Léo, Mouzard, Antoine · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2101.05020

Abstract

We define the random magnetic Laplacien with spatial white noise as magnetic field on the two-dimensional torus using paracontrolled calculus. It yields a random self-adjoint operator with pure point spectrum and domain a random subspace of nonsmooth functions in L 2. We give sharp bounds on the eigenvalues which imply an almost sure Weyl-type law.

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• Landau Hamiltonian with Gaussian white noise potential and the asymptotic of its bottom of spectrum
• Local wellposedness of the 2d Anderson-Gross-Pitaevskii equation

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