Virial expansion for almost diagonal random matrices

Details Virial expansion for almost diagonal random matrices Virial expansion for almost diagonal random matrices

2003-01-21

arxiv.org/abs/cond-mat/0301395v2

J.Phys.A36:8265-8289,2003

Physics

Condensed Matter

Disordered Systems and Neural Networks

35 pages, 10 figures, improved abstract and introduction, one more example added, typos corrected, submitted to Journal of Phy

Scientific paper

10.1088/0305-4470/36/30/305

Energy level statistics of Hermitian random matrices $\hat H$ with Gaussian independent random entries $H_{i\geq j}$ is studied for a generic ensemble of almost diagonal random matrices with $ <|H_{ii}|^{2} > \sim 1$ and $<|H_{i\neq j}|^{2} >= b {\cal F}(|i-j|) \ll 1$. We perform a regular expansion of the spectral form-factor $K(\tau) = 1 + b K_{1}(\tau) + b^{2} K_{2}(\tau) + ... $ in powers of $b \ll 1$ with the coefficients $K_{m}(\tau)$ that take into account interaction of (m+1) energy levels. To calculate $K_{m}(\tau)$, we develop a diagrammatic technique which is based on the Trotter formula and on the combinatorial problem of graph edges coloring with (m+1) colors. Expressions for $K_{1}(\tau)$ and $K_{2}(\tau)$ in terms of infinite series are found for a generic function ${\cal F}(|i-j|)$ in the Gaussian Orthogonal Ensemble (GOE), the Gaussian Unitary Ensemble (GUE) and in the crossover between them (the almost unitary Gaussian ensemble). The Rosenzweig-Porter and power-law banded matrix ensembles are considered as examples.

Affiliated with

Also associated with

No associations

Rating

Virial expansion for almost diagonal random 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 Virial expansion for almost diagonal random matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Virial expansion for almost diagonal random matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-571114