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Level Curvature Distribution and the Structure of Eigenfunctions in Disordered Systems | | C. Basu
; C.M. Canali
; V.E. Kravtsov
; I.V. Yurkevich
; | | Date: |
15 Dec 1997 | | Subject: | Mesoscopic Systems and Quantum Hall Effect | cond-mat.mes-hall | | Affiliation: | International Center for Theoretical Physics), C.M. Canali (Chalmers University of Technology), V.E. Kravtsov (International Center for Theoretical Physics and Landau Institute for Theoretical Physics), and I.V. Yurkevich (University of Birmingham | | 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 sigma-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 vector-potential 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 quasi-localized states in weakly disordered systems can cause the curvature distribution to be nonanalytic. In $2d$ 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. | | Source: | arXiv, cond-mat/9712147 | | Services: | Forum | Review | PDF | Favorites | |
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