Level curvature distribution: from bulk to the soft edge of random Hermitian matrices

Details Level curvature distribution: from bulk to the soft edge of random Hermitian matrices Level curvature distribution: from bulk to the soft edge of random Hermitian matrices

2011-08-03

arxiv.org/abs/1108.0950v1

Acta Phys. Pol. A, vol. 120, Issue 6, pages 100-113 (2012)

Physics

Mathematical Physics

The text is based on the presentation at the 5th Workshop on Quantum Chaos and Localization Phenomena, May 20-22, 2011, Warsaw

Scientific paper

Level curvature is a measure of sensitivity of energy levels of a disordered/chaotic system to perturbations. In the bulk of the spectrum Random Matrix Theory predicts the probability distributions of level curvatures to be given by Zakrzewski-Delande expressions [F. von Oppen {\it Phys. Rev. Lett.} {\bf 73} 798 (1994) & {\it Phys.Rev. E} {\bf 51} 2647 (1995); Y.V. Fyodorov and H.-J. Sommers {\it Z.Phys.B} {\bf 99} 123 (1995)]. Motivated by growing interest in statistics of extreme (maximal or minimal) eigenvalues of disordered systems of various nature, it is natural to ask about the associated level curvatures. I show how calculating the distribution for the curvatures of extreme eigenvalues in GUE ensemble can be reduced to studying asymptotic behaviour of orthogonal polynomials appearing in the recent work C. Nadal and S. N. Majumdar {\it J. Stat. Mech.} {\bf 2011} P04001 (2011). The corresponding asymptotic analysis being yet outstanding, I instead will discuss solution of a related, but somewhat simpler problem of calculating the level curvature distribution averaged over all the levels in a spectral window close to the edge of the semicircle. The method is based on asymptotic analysis of kernels associated with Hermite polynomials and their Cauchy transforms, and is straightforwardly extendable to any rotationally-invariant ensemble of random matrices.

Affiliated with

Also associated with

No associations

Rating

Level curvature distribution: from bulk to the soft edge of random Hermitian matrices 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 Level curvature distribution: from bulk to the soft edge of random Hermitian matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Level curvature distribution: from bulk to the soft edge of random Hermitian matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-13559