## Abstract

The level curvature distribution function is studied both analytically and numerically for the case of

*T*-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the random matrix theory is calculated using the nonlinear supersymmetric s model and compared to numerical simulations on the Anderson model. It is predicted analytically and confirmed numerically that the sign of the correction is different for*T*-breaking perturbations caused by a constant vectorpotential equivalent to a phase twist in the boundary conditions, and those caused by a random magnetic field. In the former case it is shown using a nonperturbative approach that quasilocalized states in weakly disordered systems can cause the curvature distribution to be nonanalytic. In two-dimensional (2D) systems the distribution function*P(K)*has a branching point at*K*=0 that is related to the multifractality of the wave functions and thus should be a generic feature of all critical eigenstates. A relationship between the branching power and the multifractality exponent*d*_{2}is suggested. Evidence of the branch-cut singularity is found in numerical simulations in 2D systems and at the Anderson transition point in 3D systems.Original language | English |
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Pages (from-to) | 14174-14191 |

Number of pages | 18 |

Journal | Physical Review B |

Volume | 57 |

Issue number | 22 |

DOIs | |

Publication status | Published - 1 Jun 1998 |