1995/03/17 by Vladimir I. Fal'ko, V. I Fal'ko, K. B. Efetov +1 · 8 citations
Materials Science · Physics and Astronomy · #Amplitude #Distribution (mathematics) #Eigenvalues and eigenvectors #Inverse #Matrix (chemical analysis) #Multifractal system #Property (philosophy) #Quantum many-body systems #Quasicrystal Structures and Properties #Random matrix #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1209/0295-5075/32/8/002
4 two-column pages, no figures, submitted to PRL.
arxiv created 1995/03/17 · openalex publication_date 1995/12/10 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05
The distribution function of local amplitudes of eigenstates of a two-dimensional disordered metal is calculated. Although the distribution of comparatively small amplitudes is governed by laws similar to those known from the random matrix theory, its decay at larger amplitudes is non-universal and, in dimension d = 2, has a logarithmically normal asymptotic dependence. The inverse participation numbers calculated on the basis of the distribution function indicate a multifractal behaviour in different fundamental symmetry classes. Our calculation is based on the derivation of the non-trivial saddle-point of the reduced supersymmetric σ-model.