[Submitted on 27 Nov 2025 (v1), last revised 30 Jul 2026 (this version, v2)]

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Abstract:We present a simple construction of a random Schrödinger operator subject to a magnetic field with a regularity as low as $0^-$-Hölder and a Gaussian white noise electric potential on a two-dimensional bounded box. This construction is based on the exponential Ansatz introduced in [HL15] and leverages the semigroup approach developed in [HL24].
The proposed construction enables us to generalise an asymptotic result for the bottom of the spectrum of the two-dimensional continuous Anderson Hamiltonian, first proved in [CvZ21], to the magnetic case. Our choice of potential not only covers the case of a uniform magnetic field, but also those which would break translational invariance.

Submission history

From: Yueh-Sheng Hsu [view email]
[v1] Thu, 27 Nov 2025 07:07:25 UTC (37 KB)
[v2] Thu, 30 Jul 2026 21:33:01 UTC (43 KB)

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