767 research outputs found
Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas
We present Quantum Monte Carlo calculations with up to N=576000 interacting
bosons in a quasi two-dimensional trap geometry closely related to recent
experiments with atomic gases. The density profile of the gas and the
non-classical moment of inertia yield intrinsic signatures for the
Kosterlitz--Thouless transition temperature T_KT. From the reduced one-body
density matrix, we compute the condensate fraction, which is quite large for
small systems. It decreases slowly with increasing system sizes, vanishing in
the thermodynamic limit. We interpret our data in the framework of the
local-density approximation, and point out the relevance of our results for the
analysis of experiments.Comment: 4 pages, 4 figure
Depinning exponents of the driven long-range elastic string
We perform a high-precision calculation of the critical exponents for the
long-range elastic string driven through quenched disorder at the depinning
transition, at zero temperature. Large-scale simulations are used to avoid
finite-size effects and to enable high precision. The roughness, growth, and
velocity exponents are calculated independently, and the dynamic and
correlation length exponents are derived. The critical exponents satisfy known
scaling relations and agree well with analytical predictions.Comment: 6 pages, 5 figure
Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?
The motion of driven interfaces in random media at finite temperature and
small external force is usually described by a linear displacement at large times, where the velocity vanishes according to the
creep formula as for . In this paper,
we question this picture on the specific example of the directed polymer in a
two dimensional random medium. We have recently shown (C. Monthus and T. Garel,
arxiv:0802.2502) that its dynamics for F=0 can be analyzed in terms of a strong
disorder renormalization procedure, where the distribution of renormalized
barriers flows towards some "infinite disorder fixed point". In the present
paper, we obtain that for small , this "infinite disorder fixed point"
becomes a "strong disorder fixed point" with an exponential distribution of
renormalized barriers. The corresponding distribution of trapping times then
only decays as a power-law , where the exponent
vanishes as as . Our
conclusion is that in the small force region , the divergence of
the averaged trapping time induces strong
non-self-averaging effects that invalidate the usual creep formula obtained by
replacing all trapping times by the typical value. We find instead that the
motion is only sub-linearly in time , i.e. the
asymptotic velocity vanishes V=0. This analysis is confirmed by numerical
simulations of a directed polymer with a metric constraint driven in a traps
landscape. We moreover obtain that the roughness exponent, which is governed by
the equilibrium value up to some large scale, becomes equal to
at the largest scales.Comment: v3=final versio
Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains
Markov-chain Monte Carlo (MCMC), the field of stochastic algorithms built on
the concept of sampling, has countless applications in science and technology.
The overwhelming majority of MCMC algorithms are time-reversible and satisfy
the detailed-balance condition, just like physical systems in thermal
equilibrium. The underlying Markov chains typically display diffusive dynamics,
which leads to a slow exploration of sample space. Significant speed-ups can be
achieved by non-reversible MCMC algorithms exhibiting non-equilibrium dynamics,
whose steady states exactly reproduce the target equilibrium states of
reversible Markov chains. Such algorithms have had successes in applications
but are generally difficult to analyze, resulting in a scarcity of exact
results. Here, we introduce the "lifted" TASEP (totally asymmetric simple
exclusion process) as a paradigm for lifted non-reversible Markov chains. Our
model can be viewed as a second-generation lifting of the reversible Metropolis
algorithm on a one-dimensional lattice and is exactly solvable by an unusual
kind of coordinate Bethe ansatz. We establish the integrability of the model
and present strong evidence that the lifting leads to faster relaxation than in
the KPZ universality class.Comment: 11 pages, 8 figure
Mean properties and Free Energy of a few hard spheres confined in a spherical cavity
We use analytical calculations and event-driven molecular dynamics
simulations to study a small number of hard sphere particles in a spherical
cavity. The cavity is taken also as the thermal bath so that the system
thermalizes by collisions with the wall. In that way, these systems of two,
three and four particles, are considered in the canonical ensemble. We
characterize various mean and thermal properties for a wide range of number
densities. We study the density profiles, the components of the local pressure
tensor, the interface tension, and the adsorption at the wall. This spans from
the ideal gas limit at low densities to the high-packing limit in which there
are significant regions of the cavity for which the particles have no access,
due the conjunction of excluded volume and confinement. The contact density and
the pressure on the wall are obtained by simulations and compared to exact
analytical results. We also obtain the excess free energy for N=4, by using a
simulated-assisted approach in which we combine simulation results with the
knowledge of the exact partition function for two and three particles in a
spherical cavity.Comment: 11 pages, 9 figures and two table
Coulomb and Liquid Dimer Models in Three Dimensions
We study classical hard-core dimer models on three-dimensional lattices using
analytical approaches and Monte Carlo simulations. On the bipartite cubic
lattice, a local gauge field generalization of the height representation used
on the square lattice predicts that the dimers are in a critical Coulomb phase
with algebraic, dipolar, correlations, in excellent agreement with our
large-scale Monte Carlo simulations. The non-bipartite FCC and Fisher lattices
lack such a representation, and we find that these models have both confined
and exponentially deconfined but no critical phases. We conjecture that
extended critical phases are realized only on bipartite lattices, even in
higher dimensions.Comment: 4 pages with corrections and update
A polynomial training algorithm for calculating perceptrons of optimal stability
Recomi (REpeated COrrelation Matrix Inversion) is a polynomially fast
algorithm for searching optimally stable solutions of the perceptron learning
problem. For random unbiased and biased patterns it is shown that the algorithm
is able to find optimal solutions, if any exist, in at worst O(N^4) floating
point operations. Even beyond the critical storage capacity alpha_c the
algorithm is able to find locally stable solutions (with negative stability) at
the same speed. There are no divergent time scales in the learning process. A
full proof of convergence cannot yet be given, only major constituents of a
proof are shown.Comment: 11 pages, Latex, 4 EPS figure
Ultracold Bosonic Atoms in Disordered Optical Superlattices
The influence of disorder on ultracold atomic Bose gases in quasiperiodic
optical lattices is discussed in the framework of the one-dimensional
Bose-Hubbard model. It is shown that simple periodic modulations of the well
depths generate a rich phase diagram consisting of superfluid, Mott insulator,
Bose-glass and Anderson localized phases. The detailed evolution of mean
occupation numbers and number fluctuations as function of modulation amplitude
and interaction strength is discussed. Finally, the signatures of the different
phases, especially of the Bose-glass phase, in matter-wave interference
experiments are investigated.Comment: 4 pages, 4 figures, using REVTEX
Aging without disorder on long time scales
We study the Metropolis dynamics of a simple spin system without disorder,
which exhibits glassy dynamics at low temperatures. We use an implementation of
the algorithm of Bortz, Kalos and Lebowitz \cite{bortz}. This method turns out
to be very efficient for the study of glassy systems, which get trapped in
local minima on many different time scales. We find strong evidence of aging
effects at low temperatures. We relate these effects to the distribution
function of the trapping times of single configurations.Comment: 8 pages Revtex, 7 figures uuencoded (Revised version: the figures are
now present
Coexistence of solutions in dynamical mean-field theory of the Mott transition
In this paper, I discuss the finite-temperature metal-insulator transition of
the paramagnetic Hubbard model within dynamical mean-field theory. I show that
coexisting solutions, the hallmark of such a transition, can be obtained in a
consistent way both from Quantum Monte Carlo (QMC) simulations and from the
Exact Diagonalization method. I pay special attention to discretization errors
within QMC. These errors explain why it is difficult to obtain the solutions by
QMC close to the boundaries of the coexistence region.Comment: 3 pages, 2 figures, RevTe
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