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• W2034376752 abstract "The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, $<psi^2_{n,mathbf{m}}>$, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions $D > 2$ one finds intervals in the energy and the disorder where extended and localized states coexist: the metal-insulator transition should thus be interpreted as a first-order transition. The qualitative differences permit to group the systems into two classes: low-dimensional systems ($2leq D leq 3$), where localized states are always exponentially localized and high-dimensional systems ($Dgeq D_c=4$), where states with non-exponential localization are also formed. The value of the upper critical dimension is found to be $D_0=6$ for the Anderson localization problem; this value is also characteristic of a related problem - percolation." @default.
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• W2034376752 date "2004-12-01" @default.
• W2034376752 modified "2023-09-27" @default.
• W2034376752 title "The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents" @default.
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• W2034376752 doi "https://doi.org/10.1140/epjb/e2005-00011-1" @default.
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