The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents

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, $$, 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 ($2\leq D \leq 3$), where localized states are always exponentially localized and high-dimensional systems ($D\geq D_c=4$), 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.Comment: 17 pages, 5 figures, to appear in Eur. Phys.J.

Application of a green's function method to the calculation of photoelectron spectra

An introduction is given to the many - body effects, which reveal themselves in photoelectron spectra, and to their origin. The consequences of these effects are discussed. The Green's function method is outlined as a tool for the accurate calculation of ionisation energies and the associated pole strengths. Applications are discussed. These include the question of the accuracy which is achieved. Formaldehyde, benzene, CS, CS2, N2, p-quinodimethane and the vibronic coupling in butatriene are given as examples

Reply to Comment on "Exact analytic solution for the generalized Lyapunov exponent of the 2-dimensional Anderson localization"

We reply to comments by P.Marko$\breve{s}$, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical assumptions made prior to the choice of the mathematical formalism. The authors of the Comment expect \emph{a priori} to see a single thermodynamic phase while our approach is capable of detecting co-existence of distinct pure phases. The limitations of the transfer matrix techniques for the multi-dimensional Anderson localization problem are discussed.Comment: 4 pages, accepted for publication in J.Phys.: Condens. Mat

Isospin mixing and energy distributions in three-body decay

The structure of the second 2$^+$ resonance in $^{6}$Li is investigated with special emphasis on its isospin 0 components. The wave functions are computed in a three-body model ($\alpha$+$n$+$p$) using the hyperspherical adiabatic expansion method combined with complex scaling. In the decay into three free particles the symmetry conserving short-range interaction dominates at short distance whereas the symmetry breaking Coulomb interaction dominates at intermediate and large distances resulting in substantial isospin mixing. We predict the mixing and the energy distributions of the fragments after decay. Computations are consistent with available experiments. We conjecture that nuclear three-body decays frequently produce such large isospin mixing at large distance where the energy distributions. are determined.Comment: 5 pages, 4 figures, to be published in Physics Letters