Expansion of a Bose-Einstein Condensate in the Presence of Disorder

Expansion of a Bose-Einstein condensate (BEC) is studied, in the presence of a random potential. The expansion is controlled by a single parameter, $(\mu\tau_{eff} /\hbar)$, where $\mu$ is the chemical potential, prior to the release of the BEC from the trap, and $\tau_{eff}$ is a transport relaxation time which characterizes the strength of the disorder. Repulsive interactions (nonlinearity) facilitate transport and can lead to diffusive spreading of the condensate which, in the absence of interactions, would have remained localized in the vicinity of its initial location

Resonances in one-dimensional Disordered Chain

We study the average density of resonances, $$, in a semi-infinite disordered chain coupled to a perfect lead. The function$$ is defined in the complex energy plane and the distance $y$ from the real axes determines the resonance width. We concentrate on strong disorder and derive the asymptotic behavior of $$ in the limit of small $y$.Comment: latex, 1 eps figure, 9 pages; v2 - final version, published in the JPhysA Special Issue Dedicated to the Physics of Non-Hermitian Operator

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

Perturbation Theory for the Rosenzweig-Porter Matrix Model

We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can be obtained within the standard framework of diagrammatic perturbation theory. The structure of the perturbation expansion allows for an interpretation of the level structure on simple physical grounds, an aspect that is missing in the exact analysis (T. Guhr, Phys. Rev. Lett. 76, 2258 (1996), T. Guhr and A. M\"uller-Groeling, cond-mat/9702113).Comment: to appear in PRE, 5 pages, REVTeX, 2 figures, postscrip

Statistics of Rare Events in Disordered Conductors

Asymptotic behavior of distribution functions of local quantities in disordered conductors is studied in the weak disorder limit by means of an optimal fluctuation method. It is argued that this method is more appropriate for the study of seldom occurring events than the approaches based on nonlinear $\sigma$-models because it is capable of correctly handling fluctuations of the random potential with large amplitude as well as the short-scale structure of the corresponding solutions of the Schr\"{o}dinger equation. For two- and three-dimensional conductors new asymptotics of the distribution functions are obtained which in some cases differ significantly from previously established results.Comment: 17 pages, REVTeX 3.0 and 1 Postscript figur

Deviations from the Gaussian distribution of mesoscopic conductance fluctuations

The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate diagrammatically the third cumulant of this distribution, the leading deviation from the Gaussian. We confirm random matrix theory calculations that the leading contribution in quasi-one dimension vanishes. However, in quasi two dimensions the third cumulant is negative, whereas in three dimensions it is positive.Comment: 9 pages, Revtex, with eps figures,to appear in Phys Rev

Correlated Evolution of Nearby Residues in Drosophilid Proteins

Here we investigate the correlations between coding sequence substitutions as a function of their separation along the protein sequence. We consider both substitutions between the reference genomes of several Drosophilids as well as polymorphisms in a population sample of Zimbabwean Drosophila melanogaster. We find that amino acid substitutions are “clustered” along the protein sequence, that is, the frequency of additional substitutions is strongly enhanced within ≈10 residues of a first such substitution. No such clustering is observed for synonymous substitutions, supporting a “correlation length” associated with selection on proteins as the causative mechanism. Clustering is stronger between substitutions that arose in the same lineage than it is between substitutions that arose in different lineages. We consider several possible origins of clustering, concluding that epistasis (interactions between amino acids within a protein that affect function) and positional heterogeneity in the strength of purifying selection are primarily responsible. The role of epistasis is directly supported by the tendency of nearby substitutions that arose on the same lineage to preserve the total charge of the residues within the correlation length and by the preferential cosegregation of neighboring derived alleles in our population sample. We interpret the observed length scale of clustering as a statistical reflection of the functional locality (or modularity) of proteins: amino acids that are near each other on the protein backbone are more likely to contribute to, and collaborate toward, a common subfunction

Numerical hydrodynamics in general relativity

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.Comment: 105 pages, 12 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.or