Level compressibility in a critical random matrix ensemble: the second virial coefficient
Abstract
We study spectral statistics of a Gaussian unitary critical ensemble of almost diagonal Hermitian random matrices with offdiagonal entries langH_{ij}^{2}rang ~ b^{2}i  j^{2} small compared to diagonal ones langH_{ii}^{2}rang ~ 1. Using the recently suggested method of virial expansion in the number of interacting energy levels (Yevtushenko and Kravtsov 2003 J. Phys. A: Math. Gen. 36 8265), we calculate a coefficient ~b^{2} Lt 1 in the level compressibility χ(b). We demonstrate that only the leading terms in χ(b) coincide for this model and for an exactly solvable model suggested by Moshe et al (1994 Phys. Rev. Lett. 73 1497), the subleading terms ~b^{2} being different. Numerical data confirm our analytical calculation.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2006
 DOI:
 10.1088/03054470/39/9/003
 arXiv:
 arXiv:condmat/0510378
 Bibcode:
 2006JPhA...39.2021K
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 several typos and the unfolding factor are corrected, Erratum has been added