Showing papers by "Pierre Le Doussal published in 2011"
TL;DR: This work provides the first exact calculation of the height distribution at arbitrary time t of the continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial conditions and obtain the generating function of the moments of the directed polymer partition sum as a Fredholm Pfaffian.
Abstract: We provide the first exact calculation of the height distribution at arbitrary time t of the continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial conditions. We use the mapping onto a directed polymer with one end fixed, one free, and the Bethe ansatz for the replicated attractive boson model. We obtain the generating function of the moments of the directed polymer partition sum as a Fredholm Pfaffian. Our formula, valid for all times, exhibits convergence of the free energy (i.e., KPZ height) distribution to the Gaussian orthogonal ensemble Tracy-Widom distribution at large time.
267 citations
TL;DR: In this paper, the authors derived the distribution of instantaneous velocities in an avalanche from the ABBM stochastic equation for a driven elastic object near depinning, and showed 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 ABBM.
Abstract: 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.
27 citations
TL;DR: A particle in one dimension submitted to amplitude and phase disorder can be mapped onto the complex Burgers equation, and provides a toy model for problems with interplay of interferences and disorder, such as the Nguyen-Spivak-Shklovskii model of hopping conductivity in disordered insulators and the Chalker-Coddington model for the (spin) quantum Hall effect.
Abstract: 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 Nguyen-Spivak-Shklovskii model of hopping conductivity in disordered insulators and the Chalker-Coddington model for the (spin) quantum Hall effect. We also propose a direct realization in an experiment with cold atoms. The model has three distinct phases: (I) a high-temperature or weak disorder phase, (II) a pinned phase for strong amplitude disorder, and (III) a 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 zeros 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.
16 citations
TL;DR: It is found that a large dissipation parameter η flows to a fixed point η(R)=η(c)=ℏ/2π and it is shown that the relaxation resistance, of recent interest, is quantized for large η.
Abstract: We study a particle on a ring in presence of a dissipative Caldeira-Leggett environment and derive its response to a dc field. We find, through a 2-loop renormalization group analysis, that a large dissipation parameter $\ensuremath{\eta}$ flows to a fixed point ${\ensuremath{\eta}}_{R}={\ensuremath{\eta}}_{c}=\ensuremath{\hbar}/2\ensuremath{\pi}$. We also reexamine the mapping of this problem to that of the Coulomb box and show that the relaxation resistance, of recent interest, is quantized for large $\ensuremath{\eta}$. For finite $\ensuremath{\eta}g{\ensuremath{\eta}}_{c}$ we find that a certain average of the relaxation resistance is quantized. We propose a box experiment to measure a quantized noise.
10 citations
01 Jan 2011
TL;DR: In this paper, an overview is given of the new theories and experiments on the phase diagram of type II superconductors, which in recent years have progressed from the Abrikosov mean field theory to the "vortex matter" picture.
Abstract: An overview is given of the new theories and experiments on the phase diagram of type II superconductors, which in recent years have progressed from the Abrikosov mean field theory to the "vortex matter" picture. We then detail some theoretical tools which allow to describe the melting of the vortex lattice, the collective pinning and creep theory, and the Bragg glass theory. It is followed by a short presentation of other glass phases of vortices, as well as phases of moving vortices.
3 citations
TL;DR: The authors 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.
Abstract: 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.
3 citations