Three-dimensional magnetic Schrödinger operator with the potential supported in a tube

2025/05/25 by Barseghyan, Diana, Bory-Reyes, Juan, Schneider, Baruch
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2505.19365

Abstract

In this paper, we study the following magnetic Schrödinger operator in ℝ³: H=(i ∇ +A)²- V, where V is non-negative potential supported over the tube built along a curve which is a local deformation of a straight one, and B:=rot(A) is a non-zero and local (i.e., a compact supported) magnetic field. Based on some new strategies, we first prove that the magnetic field does not change the essential spectrum of this system. Finally, in the last section of this paper, we establish the sufficient condition such that the discrete spectrum is empty.

Citations

• Eigenvalues of the Neumann magnetic Laplacian in the unit disk
• The magnetic Laplacian on the Disc for strong magnetic fields
• Local strong magnetic fields and the Little-Parks effect
• Magnetic Schrödinger operator with the potential supported in a curved two-dimensional strip
• On Duclos-Exner's conjecture about waveguides in strong uniform magnetic fields
• Eigenvalue bounds of the Robin Laplacian with magnetic field

Related

• Magnetic Schrödinger operator with the potential supported in a curved two-dimensional strip
• Which magnetic fields support a zero mode?
• A 3D-Schroedinger operator under magnetic steps with semiclassical applications
• Determining a magnetic Schroedinger operator from partial Cauchy data
• A quantum waveguide with Aharonov Bohm magnetic field