Critical behaviour at the metal-insulator transition in 3-dimensional disordered systems in a strong magnetic field

摘要

The critical behaviour of 3-dimensional disordered systems in a strongmagnetic field is investigated by analysing the spectral fluctuations of theenergy spectrum. The level spacing distribution $P(s)$ as well the Dyson-Mehtastatistics $\Delta_{3}(L)$ are considered. Except for the small $s$ behaviourof $P(s)$, which depends on the presence or absence of a magnetic field but noton its strength, the other quantities, large $s$ behaviour of $P(s)$ and$\Delta_{3}(L)$, turn out to be independent of its presence or absence andtherefore of the time reversal symmetry. This suggests that the metal-insulatortransition, which is defined by the symmetry of the system {\it at} thecritical point, is independent of the presence or absence of the time reversalsymmetry.