Periodic-Orbit Theory of Anderson Localization on Graphs

Details Periodic-Orbit Theory of Anderson Localization on Graphs Periodic-Orbit Theory of Anderson Localization on Graphs

1999-09-15

arxiv.org/abs/chao-dyn/9909023v2

Phys. Rev. Lett. 84 (2000) 1427-1430

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures, RevTeX

Scientific paper

10.1103/PhysRevLett.84.1427

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an a-periodic Kronig-Penney model in one dimension. The exact expression for the probability to return of an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families are performed analytically using advanced combinatorial methods.

Affiliated with

Also associated with

No associations

Rating

Periodic-Orbit Theory of Anderson Localization on Graphs 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 Periodic-Orbit Theory of Anderson Localization on Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Periodic-Orbit Theory of Anderson Localization on Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-197396