Virtual bound states of the Pauli operator with an Aharonov-Bohm potential

2025/01/28 by Fialova, Marie, Krejcirik, David · 1 voice · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2501.17029

Abstract

A maximal realisation of the two-dimensional Pauli operator, subject to Aharonov--Bohm magnetic field, is investigated. Contrary to the case of the Pauli operator with regular magnetic potentials, it is shown that both components of the Pauli operator are critical. Asymptotics of the weakly coupled eigenvalues, generated by electric (not necessarily self-adjoint) perturbations, are derived.

Cited by

• Weak coupling for Schrödinger operators with complex potentials
• Asymptotics for eigenvalues of one-dimensional Dirac operators in the weak coupling limit
• On the behavior of the ground state energy under weak perturbation of critical quasilinear operators in ℝ^N
• Cwikel-Lieb-Rozenblum type estimates for the Pauli and magnetic Schrödinger operator in dimension two

Discussions

• Marie Fialova, David Krejcirik: Virtual bound states of the Pauli operator with an Aharonov-Bohm potential https://arxiv.org/abs/2501.17029 https://arxiv.org/pdf/2501.17029 https://arxiv.org/html/2501 [bsky, 1 points, 1 comments]

Related

• Weak coupling asymptotics for the Pauli operator in two dimensions
• On the essential spectrum of two-dimensional Pauli operators with repulsive potentials
• Critical magnetic field for 2d magnetic Dirac-Coulomb operators and Hardy inequalities
• A simple criterion for the existence of nonreal eigenvalues for a class of 2D and 3D Pauli operators
• Counting Negative Eigenvalues for the Magnetic Pauli Operator