Level compressibility in a critical random matrix ensemble: The second virial coefficient
Kravtsov, Vladimir E. ; Yevtushenko, Oleg ; Cuevas, Emilio
arXiv, 0510378 / Harvested from arXiv
We study spectral statistics of a Gaussian unitary critical ensemble of almost diagonal Hermitian random matrices with off-diagonal entries $<|H_{ij}|^{2} > \sim b^{2} |i-j|^{-2}$ small compared to diagonal ones $<|H_{ii}|^{2} > \sim 1$. Using the recently suggested method of {\it virial expansion} in the number of interacting energy levels (J.Phys.A {\bf 36},8265 (2003)), we calculate a coefficient $\propto b^{2}\ll 1$ in the level compressibility $\chi(b)$. We demonstrate that only the leading terms in $\chi(b)$ coincide for this model and for an exactly solvable model suggested by Moshe, Neuberger and Shapiro (Phys.Rev.Lett. {\bf 73}, 1497 (1994)), the sub-leading terms $\sim b^{2}$ being different. Numerical data confirms our analytical calculation.
Publié le : 2005-10-14
Classification:  Condensed Matter - Disordered Systems and Neural Networks,  Condensed Matter - Mesoscale and Nanoscale Physics,  Condensed Matter - Statistical Mechanics,  Mathematical Physics
@article{0510378,
     author = {Kravtsov, Vladimir E. and Yevtushenko, Oleg and Cuevas, Emilio},
     title = {Level compressibility in a critical random matrix ensemble: The second
  virial coefficient},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0510378}
}
Kravtsov, Vladimir E.; Yevtushenko, Oleg; Cuevas, Emilio. Level compressibility in a critical random matrix ensemble: The second
  virial coefficient. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0510378/