|
|
| VOLUME 59 (1994) | ISSUE 1 |
PAGE 40
|
Level spacing distribution near the Anderson transition
Aronov A. G., Kravtsov V. E., Lerner I. V.
For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotic behavior P(s) <χ exp( — /Is2"7) for s>(i)sl, which is universal and intermediate between the Gaussian asymptotics in a metal and the Poisson asymptotics in an insulator. (Here the critical exponent is in the range 0<γ< 1, and the numerical coefficient A depends only on the dimensionality d>2.) It is obtained by mapping the energy level distribution onto the Gibbs distribution for a classical one-dimensional gas with a pairwise interaction. The interaction, which is consistent with the universal asymptotic behavior of the two-level correlation function found previously, was found to be the power-law repulsion with the exponent —γ.
|
|
Home
![](/ps/1295/article_19561_800_head.png "For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotic behavior <i>P(s) </i><χ exp( — /Is<sup>2</sup>"<sup>7</sup>) for s>(i)sl, which is universal and intermediate between the Gaussian asymptotics in a metal and the Poisson asymptotics in an insulator. (Here the critical exponent is in the range <i>0<γ< </i>1, and the numerical coefficient <i>A </i>depends only on the dimensionality <i>d>2.) </i>It is obtained by mapping the energy level distribution onto the Gibbs distribution for a classical one-dimensional gas with a pairwise interaction. The interaction, which is consistent with the universal asymptotic behavior of the two-level correlation function found previously, was found to be the power-law repulsion with the exponent <i>—γ.</i>")