Spectral shift function for operators with crossed magnetic and electric fields

We obtain a representation formula for the derivative of the spectral shift function $ξ(λ; B, ε)$ related to the operators $H_0(B,ε) = (D_x - By)^2 + D_y^2 + εx$ and $H(B, ε) = H_0(B, ε) + V(x,y), \: B > 0, ε> 0$. We establish a limiting absorption principle for $H(B, ε)$ and an estimate ${\mathcal O}(ε^{n-2})$ for $ξ'(λ; B, ε)$, provided $λ\notin σ(Q)$, where $Q = (D_x - By)^2 + D_y^2 + V(x,y).$

No reviews yet.

No comments yet.