Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards

Details Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards

2005-12-09

arxiv.org/abs/math-ph/0512030v2

Physics

Mathematical Physics

38 pages, 11 figures, version of Jan '06, in review, Comm. Pure Appl. Math

Scientific paper

The Quantum Unique Ergodicity (QUE) conjecture of Rudnick-Sarnak is that every eigenfunction phi_n of the Laplacian on a manifold with uniformly-hyperbolic geodesic flow becomes equidistributed in the semiclassical limit (eigenvalue E_n -> infinity), that is, `strong scars' are absent. We study numerically the rate of equidistribution for a uniformly-hyperbolic Sinai-type planar Euclidean billiard with Dirichlet boundary condition (the `drum problem') at unprecedented high E and statistical accuracy, via the matrix elements of a piecewise-constant test function A. By collecting 30000 diagonal elements (up to level n ~ 7*10^5) we find that their variance decays with eigenvalue as a power 0.48 +- 0.01, close to the estimate 1/2 of Feingold-Peres (FP). This contrasts the results of existing studies, which have been limited to E_n a factor 10^2 smaller. We find strong evidence for QUE in this system. We also compare off-diagonal variance, as a function of distance from the diagonal, against FP at the highest accuracy (0.7%) thus far in any chaotic system. We outline the efficient scaling method used to calculate eigenfunctions.

Affiliated with

Also associated with

No associations

Rating

Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards 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 Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-557278