28,383 research outputs found
Correlation of eigenstates in the critical regime of quantum Hall systems
We extend the multifractal analysis of the statistics of critical wave
functions in quantum Hall systems by calculating numerically the correlations
of local amplitudes corresponding to eigenstates at two different energies. Our
results confirm multifractal scaling relations which are different from those
occurring in conventional critical phenomena. The critical exponent
corresponding to the typical amplitude, , gives an almost
complete characterization of the critical behavior of eigenstates, including
correlations. Our results support the interpretation of the local density of
states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure
Microscopic dynamics of supercooled liquids from first principles
Glasses are solid materials whose constituent atoms are arranged in a
disordered manner. The transition from a liquid to a glass remains one of the
most poorly understood phenomena in condensed matter physics, and still no
fully microscopic theory exists that can describe the dynamics of supercooled
liquids in a quantitative manner over all relevant time scales. Here we present
such a theoretical framework that yields near-quantitative accuracy for the
time-dependent correlation functions of a supercooled system over a broad
density range. Our approach requires only simple static structural information
as input and is based entirely based on first principles. Owing to this
first-principles nature, the framework offers a unique platform to study the
relation between structure and dynamics in glass-forming matter, and paves the
way towards a systematically correctable and ultimately fully quantitative
theory of microscopic glassy dynamics
Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise
correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho
and the spatial dimension d. By means of a stochastic Cole-Hopf transformation,
the critical and correction-to-scaling exponents at the roughening transition
are determined to all orders in a (d - d_c) expansion. We also argue that there
is a intriguing possibility that the rough phases above and below the lower
critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead
to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett.
style files included; slightly expanded reincarnatio
Exact results for the Kardar--Parisi--Zhang equation with spatially correlated noise
We investigate the Kardar--Parisi--Zhang (KPZ) equation in spatial
dimensions with Gaussian spatially long--range correlated noise ---
characterized by its second moment --- by means of dynamic field theory and the
renormalization group. Using a stochastic Cole--Hopf transformation we derive
{\em exact} exponents and scaling functions for the roughening transition and
the smooth phase above the lower critical dimension . Below
the lower critical dimension, there is a line marking the stability
boundary between the short-range and long-range noise fixed points. For , the general structure of the renormalization-group equations
fixes the values of the dynamic and roughness exponents exactly, whereas above
, one has to rely on some perturbational techniques. We discuss the
location of this stability boundary in light of the exact results
derived in this paper, and from results known in the literature. In particular,
we conjecture that there might be two qualitatively different strong-coupling
phases above and below the lower critical dimension, respectively.Comment: 21 pages, 15 figure
Spontaneous membrane formation and self-encapsulation of active rods in an inhomogeneous motility field
We study the collective dynamics of self-propelled rods in an inhomogeneous
motility field. At the interface between two regions of constant but different
motility, a smectic rod layer is spontaneously created through aligning
interactions between the active rods, reminiscent of an artificial,
semi-permeable membrane. This "active membrane" engulfes rods which are locally
trapped in low-motility regions and thereby further enhances the trapping
efficiency by self-organization, an effect which we call "self-encapsulation".
Our results are gained by computer simulations of self-propelled rod models
confined on a two-dimensional planar or spherical surface with a stepwise
constant motility field, but the phenomenon should be observable in any
geometry with sufficiently large spatial inhomogeneity. We also discuss
possibilities to verify our predictions of active-membrane formation in
experiments of self-propelled colloidal rods and vibrated granular matter
Dielectric branes in non-trivial backgrounds
We present a procedure to evaluate the action for dielectric branes in
non-trivial backgrounds. These backgrounds must be capable to be taken into a
Kaluza-Klein form, with some non-zero wrapping factor. We derive the way this
wrapping factor is gauged away. Examples of this are AdS_5xS^5 and
AdS_3xS^3xT^4, where we perform the construction of different stable systems,
which stability relies in its dielectric character.Comment: 14 pages, published versio
Comment on ``Critical behavior of a two-species reaction-diffusion problem''
In a recent paper, de Freitas et al. [Phys. Rev. E 61, 6330 (2000)] presented
simulational results for the critical exponents of the two-species
reaction-diffusion system A + B -> 2B and B -> A in dimension d = 1. In
particular, the correlation length exponent was found as \nu = 2.21(5) in
contradiction to the exact relation \nu = 2/d. In this Comment, the symmetry
arguments leading to exact critical exponents for the universality class of
this reaction-diffusion system are concisely reconsidered
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