Spectral shift function for slowly varying perturbation of periodic Schroedinger operators

Details Spectral shift function for slowly varying perturbation of periodic Schroedinger operators Spectral shift function for slowly varying perturbation of periodic Schroedinger operators

2011-02-11

arxiv.org/abs/1102.2362v2

Mathematics

Spectral Theory

to appear in Cubo, A Mathematical Journal

Scientific paper

In this paper we study the asymptotic expansion of the spectral shift function for the slowly varying perturbations of periodic Schr\"odinger operators. We give a weak and pointwise asymptotics expansions in powers of $h$ of the derivative of the spectral shift function corresponding to the pair $\big(P(h)=P_0+\phi(hx),P_0=-\Delta+V(x)\big),$ where $\phi(x)\in {\mathcal C}^\infty(\mathbb R^n,\mathbb R)$ is a decreasing function, ${\mathcal O}(|x|^{-\delta})$ for some $\delta>n$ and $h$ is a small positive parameter. Here the potential $V$ is real, smooth and periodic with respect to a lattice $\Gamma$ in ${\mathbb R}^n$. To prove the pointwise asymptotic expansion of the spectral shift function, we establish a limiting absorption Theorem for $P(h)$.

Affiliated with

Also associated with

No associations

Rating

Spectral shift function for slowly varying perturbation of periodic Schroedinger operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spectral shift function for slowly varying perturbation of periodic Schroedinger operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral shift function for slowly varying perturbation of periodic Schroedinger operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-632514