66 research outputs found

    Diffusion in a Random Velocity Field: Spectral Properties of a Non-Hermitian Fokker-Planck Operator

    Full text link
    We study spectral properties of the Fokker-Planck operator that describes particles diffusing in a quenched random velocity field. This random operator is non-Hermitian and has eigenvalues occupying a finite area in the complex plane. We calculate the eigenvalue density and averaged one-particle Green's function, for weak disorder and dimension d>2. We relate our results to the time-evolution of particle density, and compare them with numerical simulations.Comment: 4 pages, 2 figure

    Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices

    Full text link
    We study statistical properties of the ensemble of large N×NN\times N random matrices whose entries Hij H_{ij} decrease in a power-law fashion HijâˆŒâˆŁi−jâˆŁâˆ’Î±H_{ij}\sim|i-j|^{-\alpha}. Mapping the problem onto a nonlinear σ−\sigma-model with non-local interaction, we find a transition from localized to extended states at α=1\alpha=1. At this critical value of α\alpha the system exhibits multifractality and spectral statistics intermediate between the Wigner-Dyson and Poisson one. These features are reminiscent of those typical for the mobility edge of disordered conductors. We find a continuous set of critical theories at α=1\alpha=1, parametrized by the value of the coupling constant of the σ−\sigma-model. At α>1\alpha>1 all states are expected to be localized with integrable power-law tails. At the same time, for 1<α<3/21<\alpha<3/2 the wave packet spreading at short time scale is superdiffusive: ⟹∣râˆŁâŸ©âˆŒt12α−1\langle |r|\rangle\sim t^{\frac{1}{2\alpha-1}}, which leads to a modification of the Altshuler-Shklovskii behavior of the spectral correlation function. At 1/2<α<11/2<\alpha<1 the statistical properties of eigenstates are similar to those in a metallic sample in d=(α−1/2)−1d=(\alpha-1/2)^{-1} dimensions. Finally, the region α<1/2\alpha<1/2 is equivalent to the corresponding Gaussian ensemble of random matrices (α=0)(\alpha=0). The theoretical predictions are compared with results of numerical simulations.Comment: 19 pages REVTEX, 4 figure

    Statistics of delay times in mesoscopic systems as a manifestation of eigenfunction fluctuations

    Full text link
    We reveal a general explicit relation between the statistics of delay times in one-channel reflection from a mesoscopic sample of any spatial dimension and the statistics of the eigenfunction intensities in its closed counterpart. This opens a possibility to use experimentally measurable delay times as a sensitive probe of eigenfunction fluctuations. For the particular case of quasi-one dimensional geometry of the sample we use an alternative technique to derive the probability density of partial delay times for any number of open channels.Comment: 12 pages; published version with updated reference

    Freezing of dynamical exponents in low dimensional random media

    Full text link
    A particle in a random potential with logarithmic correlations in dimensions d=1,2d=1,2 is shown to undergo a dynamical transition at Tdyn>0T_{dyn}>0. In d=1d=1 exact results demonstrate that Tdyn=TcT_{dyn}=T_c, the static glass transition temperature, and that the dynamical exponent changes from z(T)=2+2(Tc/T)2z(T)=2 + 2 (T_c/T)^2 at high temperature to z(T)=4Tc/Tz(T)= 4 T_c/T in the glass phase. The same formulae are argued to hold in d=2d=2. Dynamical freezing is also predicted in the 2D random gauge XY model and related systems. In d=1d=1 a mapping between dynamics and statics is unveiled and freezing involves barriers as well as valleys. Anomalous scaling occurs in the creep dynamics.Comment: 5 pages, 2 figures, RevTe

    Random Dirac Fermions and Non-Hermitian Quantum Mechanics

    Full text link
    We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian operator can be obtained as the solution to a two-dimensional Dirac equation in the presence of a random gauge field. Consequences for the localization properties and the critical nature of the states are discussed.Comment: 5 pages, Latex, 1 figure, version published in PR

    Anderson Transitions

    Get PDF
    The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians. Analytical approaches are complemented by advanced numerical simulations.Comment: 63 pages, 39 figures, submitted to Rev. Mod. Phy

    Haloes gone MAD: The Halo-Finder Comparison Project

    Full text link
    [abridged] We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends (FOF), spherical-overdensity (SO) and phase-space based algorithms. We further introduce a robust (and publicly available) suite of test scenarios that allows halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large-scale structure of the universe. All the halo finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Via a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 30-40 particles. However, also here the phase space finders excelled by resolving substructure down to 10-20 particles. By comparing the halo finders using a high resolution cosmological volume we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity, and peak of the rotation curve).Comment: 27 interesting pages, 20 beautiful figures, and 4 informative tables accepted for publication in MNRAS. The high-resolution version of the paper as well as all the test cases and analysis can be found at the web site http://popia.ft.uam.es/HaloesGoingMA

    Observational evidence for gravitationally trapped massive axion(-like) particles

    Full text link
    Unexpected astrophysical observations can be explained by gravitationally captured massive particles, which are produced inside the Sun or other Stars and are accumulated over cosmic times. Their radiative decay in solar outer space would give rise to a `self-irradiation' of the whole star, providing the time-independent component of the corona heating source. In analogy with the Sun-irradiated Earth atmosphere, the temperature and density gradient in the corona - chromosphere transition region is suggestive for an omnipresent irradiation of the Sun. The same scenario fits other astrophysical X-ray observations. The radiative decay of a population of such elusive particles mimics a hot gas. X-ray observatories, with an unrivalled sensitivity below ~10 keV, can search for such particles. The elongation angle relative to the Sun is the relevant new parameter.Comment: 35 pages, LaTeX, 9 figures. Accepted by Astroparticle Physic

    The Circumgalactic Medium in Massive Halos

    Full text link
    This chapter presents a review of the current state of knowledge on the cool (T ~ 1e4 K) halo gas content around massive galaxies at z ~ 0.2-2. Over the last decade, significant progress has been made in characterizing the cool circumgalactic gas in massive halos of Mh ~ 1e12-1e14 Msun at intermediate redshifts using absorption spectroscopy. Systematic studies of halo gas around massive galaxies beyond the nearby universe are made possible by large spectroscopic samples of galaxies and quasars in public archives. In addition to accurate and precise constraints for the incidence of cool gas in massive halos, detailed characterizations of gas kinematics and chemical compositions around massive quiescent galaxies at z ~ 0.5 have also been obtained. Combining all available measurements shows that infalling clouds from external sources are likely the primary source of cool gas detected at d >~ 100 kpc from massive quiescent galaxies. The origin of the gas closer in is currently less certain, but SNe Ia driven winds appear to contribute significantly to cool gas found at d < 100 kpc. In contrast, cool gas observed at d <~ 200 kpc from luminous quasars appears to be intimately connected to quasar activities on parsec scales. The observed strong correlation between cool gas covering fraction in quasar host halos and quasar bolometric luminosity remains a puzzle. Combining absorption-line studies with spatially-resolved emission measurements of both gas and galaxies is the necessary next step to address remaining questions.Comment: 29 pages, 7 figures, invited review to appear in "Gas Accretion onto Galaxies", Astrophysics and Space Science Library, eds. A. Fox & R. Dave, to be published by Springe
    • 

    corecore