Spectral shift function for operators with crossed magnetic and electric fields

Abstract

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

Cited by in corpus (4)

• Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian
• Spectral problems for operators with crossed magnetic and electric fields
• Absence of embedded eigenvalues for Hamiltonian with crossed magnetic and electric fields
• Some applications of almost analytic extensions to operator bounds in trace ideals