1,074 research outputs found
Distribution of velocities in an avalanche
For a driven elastic object near depinning, we derive from first principles
the distribution of instantaneous velocities in an avalanche. We prove that
above the upper critical dimension, d >= d_uc, the n-times distribution of the
center-of-mass velocity is equivalent to the prediction from the ABBM
stochastic equation. Our method allows to compute space and time dependence
from an instanton equation. We extend the calculation beyond mean field, to
lowest order in epsilon=d_uc-d.Comment: 4 pages, 2 figure
Super-rough phase of the random-phase sine-Gordon model: Two-loop results
We consider the two-dimensional random-phase sine-Gordon and study the
vicinity of its glass transition temperature , in an expansion in small
, where denotes the temperature. We derive
renormalization group equations in cubic order in the anharmonicity, and show
that they contain two universal invariants. Using them we obtain that the
correlation function in the super-rough phase for temperature behaves
at large distances as , where the amplitude
is a universal function of temperature
. This result differs at
two-loop order, i.e., , from the prediction based on
results from the "nearly conformal" field theory of a related fermion model. We
also obtain the correction-to-scaling exponent.Comment: 34 page
Shock statistics in higher-dimensional Burgers turbulence
We conjecture the exact shock statistics in the inviscid decaying Burgers
equation in D>1 dimensions, with a special class of correlated initial
velocities, which reduce to Brownian for D=1. The prediction is based on a
field-theory argument, and receives support from our numerical calculations. We
find that, along any given direction, shocks sizes and locations are
uncorrelated.Comment: 4 pages, 8 figure
Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities
We reveal a phase transition with decreasing viscosity at \nu=\nu_c>0
in one-dimensional decaying Burgers turbulence with a power-law correlated
random profile of Gaussian-distributed initial velocities
\sim|x-x'|^{-2}. The low-viscosity phase exhibits non-Gaussian
one-point probability density of velocities, continuously dependent on \nu,
reflecting a spontaneous one step replica symmetry breaking (RSB) in the
associated statistical mechanics problem. We obtain the low orders cumulants
analytically. Our results, which are checked numerically, are based on
combining insights in the mechanism of the freezing transition in random
logarithmic potentials with an extension of duality relations discovered
recently in Random Matrix Theory. They are essentially non mean-field in nature
as also demonstrated by the shock size distribution computed numerically and
different from the short range correlated Kida model, itself well described by
a mean field one step RSB ansatz. We also provide some insights for the finite
viscosity behaviour of velocities in the latter model.Comment: Published version, essentially restructured & misprints corrected. 6
pages, 5 figure
Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows
We use renormalization group methods to derive equations of motion for large
scale variables in fluid dynamics. The large scale variables are averages of
the underlying continuum variables over cubic volumes, and naturally live on a
lattice. The resulting lattice dynamics represents a perfect discretization of
continuum physics, i.e. grid artifacts are completely eliminated. Perfect
equations of motion are derived for static, slow flows of incompressible,
viscous fluids. For Hagen-Poiseuille flow in a channel with square cross
section the equations reduce to a perfect discretization of the Poisson
equation for the velocity field with Dirichlet boundary conditions. The perfect
large scale Poisson equation is used in a numerical simulation, and is shown to
represent the continuum flow exactly. For non-square cross sections we use a
numerical iterative procedure to derive flow equations that are approximately
perfect.Comment: 25 pages, tex., using epsfig, minor changes, refernces adde
Avalanches in mean-field models and the Barkhausen noise in spin-glasses
We obtain a general formula for the distribution of sizes of "static
avalanches", or shocks, in generic mean-field glasses with
replica-symmetry-breaking saddle points. For the Sherrington-Kirkpatrick (SK)
spin-glass it yields the density rho(S) of the sizes of magnetization jumps S
along the equilibrium magnetization curve at zero temperature. Continuous
replica-symmetry breaking allows for a power-law behavior rho(S) ~ 1/(S)^tau
with exponent tau=1 for SK, related to the criticality (marginal stability) of
the spin-glass phase. All scales of the ultrametric phase space are implicated
in jump events. Similar results are obtained for the sizes S of static jumps of
pinned elastic systems, or of shocks in Burgers turbulence in large dimension.
In all cases with a one-step solution, rho(S) ~ S exp(-A S^2). A simple
interpretation relating droplets to shocks, and a scaling theory for the
equilibrium analog of Barkhausen noise in finite-dimensional spin glasses are
discussed.Comment: 6 pages, 1 figur
Free-energy distribution of the directed polymer at high temperature
We study the directed polymer of length in a random potential with fixed
endpoints in dimension 1+1 in the continuum and on the square lattice, by
analytical and numerical methods. The universal regime of high temperature
is described, upon scaling 'time' and space (with for the discrete model) by a continuum model with
-function disorder correlation. Using the Bethe Ansatz solution for the
attractive boson problem, we obtain all positive integer moments of the
partition function. The lowest cumulants of the free energy are predicted at
small time and found in agreement with numerics. We then obtain the exact
expression at any time for the generating function of the free energy
distribution, in terms of a Fredholm determinant. At large time we find that it
crosses over to the Tracy Widom distribution (TW) which describes the fixed
infinite limit. The exact free energy distribution is obtained for any time
and compared with very recent results on growth and exclusion models.Comment: 6 pages, 3 figures large time limit corrected and convergence to
Tracy Widom established, 1 figure changed
QCD as a Quantum Link Model
QCD is constructed as a lattice gauge theory in which the elements of the
link matrices are represented by non-commuting operators acting in a Hilbert
space. The resulting quantum link model for QCD is formulated with a fifth
Euclidean dimension, whose extent resembles the inverse gauge coupling of the
resulting four-dimensional theory after dimensional reduction. The inclusion of
quarks is natural in Shamir's variant of Kaplan's fermion method, which does
not require fine-tuning to approach the chiral limit. A rishon representation
in terms of fermionic constituents of the gluons is derived and the quantum
link Hamiltonian for QCD with a U(N) gauge symmetry is expressed in terms of
glueball, meson and constituent quark operators. The new formulation of QCD is
promising both from an analytic and from a computational point of view.Comment: 27 pages, including three figures. ordinary LaTeX; Submitted to Nucl.
Phys.
Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet
Identifying the correct low-energy effective theory for magnons and holes in
an antiferromagnet has remained an open problem for a long time. In analogy to
the effective theory for pions and nucleons in QCD, based on a symmetry
analysis of Hubbard and t-J-type models, we construct a systematic low-energy
effective field theory for magnons and holes located inside pockets centered at
lattice momenta (\pm pi/2a,\pm pi/2a). The effective theory is based on a
nonlinear realization of the spontaneously broken spin symmetry and makes
model-independent universal predictions for the entire class of lightly doped
antiferromagnetic precursors of high-temperature superconductors. The
predictions of the effective theory are exact, order by order in a systematic
low-energy expansion. We derive the one-magnon exchange potentials between two
holes in an otherwise undoped system. Remarkably, in some cases the
corresponding two-hole Schr\"odinger equations can even be solved analytically.
The resulting bound states have d-wave characteristics. The ground state wave
function of two holes residing in different hole pockets has a d_{x^2-y^2}-like
symmetry, while for two holes in the same pocket the symmetry resembles d_{xy}.Comment: 35 pages, 11 figure
Interference in disordered systems: A particle in a complex random landscape
We consider a particle in one dimension submitted to amplitude and phase
disorder. It can be mapped onto the complex Burgers equation, and provides a
toy model for problems with interplay of interferences and disorder, such as
the NSS model of hopping conductivity in disordered insulators and the
Chalker-Coddington model for the (spin) quantum Hall effect. The model has
three distinct phases: (I) a {\em high-temperature} or weak disorder phase,
(II) a {\em pinned} phase for strong amplitude disorder, and (III) a {\em
diffusive} phase for strong phase disorder, but weak amplitude disorder. We
compute analytically the renormalized disorder correlator, equivalent to the
Burgers velocity-velocity correlator at long times. In phase III, it assumes a
universal form. For strong phase disorder, interference leads to a logarithmic
singularity, related to zeroes of the partition sum, or poles of the complex
Burgers velocity field. These results are valuable in the search for the
adequate field theory for higher-dimensional systems.Comment: 16 pages, 7 figure
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