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

Comment on ``Critical Behavior in Disordered Quantum Systems Modified by Broken Time--Reversal Symmetry''

In a recent Letter [Phys. Rev. Lett. 80, 1003 (1998)] Hussein and Pato employed the maximum entropy principle (MEP) in order to derive interpolating ensembles between any pair of universality classes in random matrix theory. They apply their formalism also to the transition from random matrix to Poisson statistics of spectra that is observed for the case of the Anderson-type metal-insulator transition. We point out the problems with the latter procedure.Comment: 1 page in PS, to appear in PRL Sept. 2

Borromean Binding of Three or Four Bosons

We estimate the ratio $R=g_{3}/g_{2}$ of the critical coupling constants $g_{2}$ and $g_{3}$ which are required to achieve binding of 2 or 3 bosons, respectively, with a short-range interaction, and examine how this ratio depends on the shape of the potential. Simple monotonous potentials give $R\simeq 0.8$. A wide repulsive core pushes this ratio close to R=1. On the other hand, for an attractive well protected by an external repulsive barrier, the ratio approaches the rigorous lower bound $R=2/3$. We also present results for N=4 bosons, sketch the extension to $N>4$, and discuss various consequences.Comment: 12 pages, RevTeX, 5 Figures in tex include

Nomenclature and Terminology of Organic Chemistry. I. Sixty Years of Croatian Nomenclature of Organic Chemistry

U ovomu je članku opisana povijest i razvitak hrvatske nomenklature organskih spojeva - od prvoga hrvatskog prijevoda međunarodnih nomenklaturnih preporuka do današnjih dana. U uvodnome dijelu definirana su trivijalna, uvriježena, sustavna (racionalna) i polusustavna imena te je rastumačena etimologija i značenje pojmova nomenklatura i terminologija i njihovih prevedenica imenje i nazivlje. U središnjem poglavlju ukazano je na potrebu osmišljavanja naše nacionalne nomenklature, što je uočeno već 1952. u HKD-u, a rezultat je bio prijevod izvornika Ženevskih pravila (1892.) i Lieške nomenklature (1930.) tiskan 1954. Potom je 1979. objavljen izvornik IUPAC-ove Plave knjige, koja sadrži iscrpna nova pravila imenovanja organskih spojeva, a njezino je prevođenje potaknuo SKTH (današnji HDKI). Hrvatsko izdanje toga važnog dokumenta objavljeno je u dva dijela (1985. i 1988.). Sljedeći važan naslov kojim se olakšava snalaženje u tim složenim pravilima, i donekle ih izmjenjuje, jest Vodič kroz IUPAC-ovu nomenklaturu organske kemije, čiji je izvornik iz 1993. na hrvatski preveden godine 2002. Osim tri nabrojana djela, objavljeni su hrvatski prijevodi gotovo pedeset dokumenata iz nomenklature pojedinih razreda organskih spojeva, od kojih većina predstavlja preporuke HKD-a i SKTH-a (HDKI). Na kraju središnjeg poglavlja analizirana je nomenklatura u prijevodima pet opsežnih sveučilišnih udžbenika u razdoblju od 1968. do danas, koja je više-manje usklađena s IUPAC-ovim preporukama iz vremenanjihova izdavanja. U zaključku se naglašava da se postojeća IUPAC-ova pravila primjenjuju u srednjoškolskoj i sveučilišnoj nastavi te u enciklopedistici i većini sredstava javnog priopćivanja.This article describes the history and development of the Croatian nomenclature of organic chemistry from the publication of the first translation of international nomenclature recommendations to the present age. In the Introduction, trivial, common, systematic (rational), and semisystematic names are defined, and the etymology and meaning of terms nomenclature and terminology are clarified. At the beginning of the central part of this article, attention is focused on the need to create our national nomenclature. The very first such project, initiated by the Croatian Chemical Society (CCS), was the translation of the Geneva (1892) and Lie`ge rules (1930) published in 1954. In 1979 comprehensive general IUPAC rules appeared, and the Croatian Society of Chemical Engineers (CSCE) in two volumes printed the Croatian edition of this important document, known as the Blue Book, in 1985 and 1988. A Guide to IUPAC Nomenclature of Organic Compounds (1993) expanded the main principles and rules from the Blue Book, and introduced a higher degree of organic nomenclature systematization. The Croatian translation of the Guide was published in 2002. In the last six decades, almost fifty translations of international rules have been issued, and almost all of them represented the official recommendations of the CCS/CSCE. Finally, the nomenclature in the translations of five comprehensive textbooks for organic chemistry is analysed. In conclusion, readers are informed that the Croatian version of IUPAC rules is applied in our secondary school and university education, in Croatian encyclopaedism and mass media, as well

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

Spectral Properties of the Chalker-Coddington Network

We numerically investigate the spectral statistics of pseudo-energies for the unitary network operator U of the Chalker--Coddington network. The shape of the level spacing distribution as well the scaling of its moments is compared to known results for quantum Hall systems. We also discuss the influence of multifractality on the tail of the spacing distribution.Comment: JPSJ-style, 7 pages, 4 Postscript figures, to be published in J. Phys. Soc. Jp

Anomalously large critical regions in power-law random matrix ensembles

We investigate numerically the power-law random matrix ensembles. Wavefunctions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 in the localized phase and 0.5 in the extended phase. The characteristic length is so anomalously large that for macroscopic samples there exists a finite critical region, in which this length is larger than the system size. The Green's functions decrease with distance as a power law with an exponent related to the correlation dimension.Comment: RevTex, 4 pages, 4 eps figures. Final version to be published in Phys. Rev. Let