On Concrete Spectral Properties of a Twisted Laplacian Associated with a Central Extension of the Real Heisenberg Group. (20th August 2017) - El Fardi, Aymane; Ghanmi, Allal; Intissar, Ahmed
Abstract : We consider the special magnetic Laplacian given by Δ ν, μ = 4 ∑ j = 1 n ∂ 2 / ∂ z j ∂ z j ¯ + 2 i ν E + E ¯ + n + 2 μ E - E ¯ - ν 2 + μ 2 z 2 . We show that Δ ν, μ is connected to the sub-Laplacian of a group of Heisenberg type given by C   × ω   C n realized as a central extension of the real Heisenberg group H 2 n + 1 . We also discuss invariance properties of Δ ν, μ and give some of their explicit spectral properties.