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math.AP2026
Time dependent Schrödinger equation for harmonic oscillator in the Aharonov-Bohm magnetic field
Jiyu Fan, Ari Laptev
We construct an approximation of the kernel of the solution of the time dependent Schrödinger equation whose Hamiltonian is a 2D harmonic oscillator in Aharonov-Bohm magnetic fiel…
math.AP2024
Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups
Rupert L. Frank, Bernard Helffer, Ari Laptev
We show that the -th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the -st Neumann eigenvalue. This extends earlier results i…