340 research outputs found
Anomalous Drude Model
A generalization of the Drude model is studied. On the one hand, the free
motion of the particles is allowed to be sub- or superdiffusive; on the other
hand, the distribution of the time delay between collisions is allowed to have
a long tail and even a non-vanishing first moment. The collision averaged
motion is either regular diffusive or L\'evy-flight like. The anomalous
diffusion coefficients show complex scaling laws. The conductivity can be
calculated in the diffusive regime. The model is of interest for the
phenomenological study of electronic transport in quasicrystals.Comment: 4 pages, latex, 2 figures, to be published in Physical Review Letter
Distance traveled by random walkers before absorption in a random medium
We consider the penetration length of random walkers diffusing in a
medium of perfect or imperfect absorbers of number density . We solve
this problem on a lattice and in the continuum in all dimensions , by means
of a mean-field renormalization group. For a homogeneous system in , we
find that , where is the absorber density
correlation length. The cases of D=1 and D=2 are also treated. In the presence
of long-range correlations, we estimate the temporal decay of the density of
random walkers not yet absorbed. These results are illustrated by exactly
solvable toy models, and extensive numerical simulations on directed
percolation, where the absorbers are the active sites. Finally, we discuss the
implications of our results for diffusion limited aggregation (DLA), and we
propose a more effective method to measure in DLA clusters.Comment: Final version: also considers the case of imperfect absorber
Theory of the temperature and doping dependence of the Hall effect in a model with x-ray edge singularities in d=oo
We explain the anomalous features in the Hall data observed experimentally in
the normal state of the high-Tc superconductors. We show that a consistent
treatment of the local spin fluctuations in a model with x-ray edge
singularities in d=oo reproduces the temperature and the doping dependence of
the Hall constant as well as the Hall angle in the normal state. The model has
also been invoked to justify the marginal-Fermi-liquid behavior, and provides a
consistent explanation of the Hall anomalies for a non-Fermi liquid in d=oo.Comment: 5 pages, 4 figures, To appear in Phys. Rev. B, title correcte
Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion
For a specific choice of the diffusion, the parabolic-elliptic
Patlak-Keller-Segel system with non-linear diffusion (also referred to as the
quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold
phenomenon: there is a critical mass such that all the solutions with
initial data of mass smaller or equal to exist globally while the
solution blows up in finite time for a large class of initial data with mass
greater than . Unlike in space dimension 2, finite mass self-similar
blowing-up solutions are shown to exist in space dimension
Anisotropic Coarsening: Grain Shapes and Nonuniversal Persistence
We solve a coarsening system with small but arbitrary anisotropic surface
tension and interface mobility. The resulting size-dependent growth shapes are
significantly different from equilibrium microcrystallites, and have a
distribution of grain sizes different from isotropic theories. As an
application of our results, we show that the persistence decay exponent depends
on anisotropy and hence is nonuniversal.Comment: 4 pages (revtex), 2 eps figure
Self-gravitating Brownian particles in two dimensions: the case of N=2 particles
We study the motion of N=2 overdamped Brownian particles in gravitational
interaction in a space of dimension d=2. This is equivalent to the simplified
motion of two biological entities interacting via chemotaxis when time delay
and degradation of the chemical are ignored. This problem also bears some
similarities with the stochastic motion of two point vortices in viscous
hydrodynamics [Agullo & Verga, Phys. Rev. E, 63, 056304 (2001)]. We
analytically obtain the density probability of finding the particles at a
distance r from each other at time t. We also determine the probability that
the particles have coalesced and formed a Dirac peak at time t (i.e. the
probability that the reduced particle has reached r=0 at time t). Finally, we
investigate the variance of the distribution and discuss the proper form
of the virial theorem for this system. The reduced particle has a normal
diffusion behaviour for small times with a gravity-modified diffusion
coefficient =r_0^2+(4k_B/\xi\mu)(T-T_*)t, where k_BT_{*}=Gm_1m_2/2 is a
critical temperature, and an anomalous diffusion for large times
~t^(1-T_*/T). As a by-product, our solution also describes the growth of
the Dirac peak (condensate) that forms in the post-collapse regime of the
Smoluchowski-Poisson system (or Keller-Segel model) for T<T_c=GMm/(4k_B). We
find that the saturation of the mass of the condensate to the total mass is
algebraic in an infinite domain and exponential in a bounded domain.Comment: Revised version (20/5/2010) accepted for publication in EPJ
Analytical results for random walk persistence
In this paper, we present the detailed calculation of the persistence
exponent for a nearly-Markovian Gaussian process , a problem
initially introduced in [Phys. Rev. Lett. 77, 1420 (1996)], describing the
probability that the walker never crosses the origin. New resummed perturbative
and non-perturbative expressions for are obtained, which suggest a
connection with the result of the alternative independent interval
approximation (IIA). The perturbation theory is extended to the calculation of
for non-Gaussian processes, by making a strong connection between the
problem of persistence and the calculation of the energy eigenfunctions of a
quantum mechanical problem. Finally, we give perturbative and non-perturbative
expressions for the persistence exponent , describing the
probability that the process remains bigger than .Comment: 23 pages; accepted for publication to Phys. Rev. E (Dec. 98
Asymptotically exact solution of a local copper-oxide model
We present an asymptotically exact solution of a local copper-oxide model
abstracted from the multi-band models. The phase diagram is obtained through
the renormalization-group analysis of the partition function. In the strong
coupling regime, we find an exactly solved line, which crosses the quantum
critical point of the mixed valence regime separating two different
Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is
formed near the chemical potential, and a marginal-FL spectrum can be derived
for the spin and charge susceptibilities.Comment: 11 pages, 1 postcript figure is appended as self-extracting archive,
Revtex 2.0, ICTP preprint 199
Post-collapse dynamics of self-gravitating Brownian particles in D dimensions
We address the post-collapse dynamics of a self-gravitating gas of Brownian
particles in D dimensions, in both canonical and microcanonical ensembles. In
the canonical ensemble, the post-collapse evolution is marked by the formation
of a Dirac peak with increasing mass. The density profile outside the peak
evolves self-similarly with decreasing central density and increasing core
radius. In the microcanonical ensemble, the post-collapse regime is marked by
the formation of a ``binary''-like structure surrounded by an almost uniform
halo with high temperature. These results are consistent with thermodynamical
predictions
Anomalous Resonance of the Symmetric Single-Impurity Anderson Model in the Presence of Pairing Fluctuations
We consider the symmetric single-impurity Anderson model in the presence of
pairing fluctuations. In the isotropic limit, the degrees of freedom of the
local impurity are separated into hybridizing and non-hybridizing modes. The
self-energy for the hybridizing modes can be obtained exactly, leading to two
subbands centered at . For the non-hybridizing modes, the second order
perturbation yields a singular resonance of the marginal Fermi liquid form. By
multiplicative renomalization, the self-energy is derived exactly, showing the
resonance is pinned at the Fermi level, while its strength is weakened by
renormalization.Comment: 4 pages, revtex, no figures. To be published in Physical Review
Letter
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