Equality of the Spectral and Dynamical Definitions of Reflection

Details Equality of the Spectral and Dynamical Definitions of Reflection Equality of the Spectral and Dynamical Definitions of Reflection

2009-05-22

arxiv.org/abs/0905.3724v1

Physics

Mathematical Physics

Scientific paper

For full-line Jacobi matrices, Schr\"odinger operators, and CMV matrices, we show that being reflectionless, in the sense of the well-known property of $m$-functions, is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to $x=-\infty$ as $t\to -\infty $ goes entirely to $x=\infty$ as $t\to\infty$. This allows us to settle a conjecture of Deift and Simon from 1983 regarding ergodic Jacobi matrices.

Affiliated with

Also associated with

No associations

Rating

Equality of the Spectral and Dynamical Definitions of Reflection 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 Equality of the Spectral and Dynamical Definitions of Reflection, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equality of the Spectral and Dynamical Definitions of Reflection will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-325854