Information Length and Localization in One Dimension

The scaling properties of the wave functions in finite samples of the one dimensional Anderson model are analyzed. The states have been characterized using a new form of the information or entropic length, and compared with analytical results obtained by assuming an exponential envelope function. A perfect agreement is obtained already for systems of $10^3$--$10^4$ sites over a very wide range of disorder parameter $10^{-4}<W<10^4$. Implications for higher dimensions are also presented.Comment: 11 pages (+3 Figures upon request), Plain TE

Multifractality beyond the Parabolic Approximation: Deviations from the Log-normal Distribution at Criticality in Quantum Hall Systems

Based on differences of generalized R\'enyi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two--measure random Cantor set are calculated exactly and finally using the results of numerical simulations the distribution of the eigenvector components calculated in the critical region of the lowest Landau--band is analyzed.Comment: LaTeX 4 pages, 3 EPS included, to appear in Europhysics Letter

One-parameter superscaling in three dimensions

Numerical and analytical details are presented on the newly discovered superscaling property of the energy spacing distribution in the three dimensional Anderson model.Comment: 4 pages, 3 figure

The generalized localization lengths in one dimensional systems with correlated disorder

The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared. Generalized entropic localization lengths are introduced in order to characterize the states and compared with their behavior for exponential localization. An acceptable agreement is obtained, however, the exponential form seems to be an oversimplification in the presence of correlated disorder. According to our analysis in the case of the random dimer model and the two new models the presence of power-law localization cannot be ruled out.Comment: 7 pages, LaTeX (IOP style), 2 figure

On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems

We discuss some properties of the generalized entropies, called Renyi entropies and their application to the case of continuous distributions. In particular it is shown that these measures of complexity can be divergent, however, their differences are free from these divergences thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e. to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e. no classical limit can be defined. Numerical simulations on a one dimensional disordered system corroborate our expectations.Comment: 8 pages with 2 embedded eps figures, RevTex4, AmsMath included, submitted to PR

QUANTUM CHEMICAL INTERPRETATION OF THE REACTION BETWEEN L-ASCORBIC ACID AND FORMALDEHYDE AND ITS BIOLOGICAL SIGNIFICANCE

We have recognized a new nucleophilic addition reaction between L-ascorbic acid and formaldehyde in biological circumstances (pH 7.4, T = 300 K). UV spectroscopic investi- gation showed that the C2=C3 double bond of ascorbic acid rapidly disappears during the reaction, verifying that the addition breaks the double bond. On the other hand, 13C NMR studies have proved that on atom C2 an additional C-C single bond is formed. Ex- act interpretation of the reaction mechanism is possible only by using quantum chemical argumentations. Ab initio calculations show that in ionized (anionic) form of L-ascorbic acid in water solution the Mulliken excess atomic charge is strongly negative on atom C2 while C1 and C3 exhibit significant positive net charges. Coulombic attraction arranges formaldehyde's C=O double bond over the C2=C3 double bond of ascorbic acid and the interaction of the two loose π-electron systems causes forming of a new σ C-C bond. The described reaction plays a protective role in biological systems, since in this way the toxic carcinogenic formaldehyde can be eliminated