Regularity of Eigenstates in Regular Mourre Theory

Details Regularity of Eigenstates in Regular Mourre Theory Regularity of Eigenstates in Regular Mourre Theory

2010-06-02

arxiv.org/abs/1006.0410v2

Physics

Mathematical Physics

27 pages

Scientific paper

The present paper gives an abstract method to prove that possibly embedded eigenstates of a self-adjoint operator $H$ lie in the domain of the $k^{th}$ power of a conjugate operator $A$. Conjugate means here that $H$ and $A$ have a positive commutator locally near the relevant eigenvalue in the sense of Mourre. The only requirement is $C^{k+1}(A)$ regularity of $H$. Regarding integer $k$, our result is optimal. Under a natural boundedness assumption of the multiple commutators we prove that the eigenstate 'dilated' by $\exp(i\theta A)$ is analytic in a strip around the real axis. In particular, the eigenstate is an analytic vector with respect to $A$. Natural applications are 'dilation analytic' systems satisfying a Mourre estimate, where our result can be viewed as an abstract version of a theorem due to Balslev and Combes. As a new application we consider the massive Spin-Boson Model.

Affiliated with

Also associated with

No associations

Rating

Regularity of Eigenstates in Regular Mourre Theory 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 Regularity of Eigenstates in Regular Mourre Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularity of Eigenstates in Regular Mourre Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-512976