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Clément Sire

Publications and source records attributed to Clément Sire.

34 records · Page 2Linked to original sources
arXiv2010

Quantum Critical Scaling of Fidelity Susceptibility

The behavior of the ground-state fidelity susceptibility in the vicinity of a quantum critical point is investigated. We derive scaling relations describing its singular behavior in the quantum critical regime. Unlike it has been found in previous studies, these relations are solely expressed in terms of conventional critical exponents. We also describe in detail a quantum Monte Carlo scheme that allows for the evaluation of the fidelity susceptibility for a large class of many-body systems and apply it in the study of the quantum phase transition for the transverse-field Ising model on the square lattice. Finite size analysis applied to the so obtained numerical results confirm the validity of our scaling relations. Furthermore, we analyze the properties of a closely related quantity, the ground-state energy's second derivative, that can be numerically evaluated in a particularly efficient way. The usefulness of both quantities as alternative indicators of quantum criticality is examined.

cond-mat.str-el↗
arXiv2008

Contest based on a directed polymer in a random medium

We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At his turn, each of the two players picks a move among two alternatives in order to maximize his final score, and minimize opponent's return. For a game of length $n$, we find that the probability distribution of the final score $S_n$ develops a traveling wave form, ${\rm Prob}(S_n=m)=f(m-v n)$, with the wave profile $f(z)$ unusually decaying as a double exponential for large positive and negative $z$. In addition, as the only parameter in the game is varied, we find a transition where one player is able to get his maximum theoretical score. By extending this model, we suggest that the front velocity $v$ is selected by the nonlinear marginal stability mechanism arising in some traveling wave problems for which the profile decays exponentially, and for which standard traveling wave theory applies.

cond-mat.stat-mech↗
arXiv2008

Crossing intervals of non-Markovian Gaussian processes

We review the properties of time intervals between the crossings at a level M of a smooth stationary Gaussian temporal signal. The distribution of these intervals and the persistence are derived within the Independent Interval Approximation (IIA). These results grant access to the distribution of extrema of a general Gaussian process. Exact results are obtained for the persistence exponents and the crossing interval distributions, in the limit of large |M|. In addition, the small time behavior of the interval distributions and the persistence is calculated analytically, for any M. The IIA is found to reproduce most of these exact results and its accuracy is also illustrated by extensive numerical simulations applied to non-Markovian Gaussian processes appearing in various physical contexts.

cond-mat.stat-mech↗
arXiv2007

Universal statistical properties of poker tournaments

We present a simple model of Texas hold'em poker tournaments which retains the two main aspects of the game: i. the minimal bet grows exponentially with time; ii. players have a finite probability to bet all their money. The distribution of the fortunes of players not yet eliminated is found to be independent of time during most of the tournament, and reproduces accurately data obtained from Internet tournaments and world championship events. This model also makes the connection between poker and the persistence problem widely studied in physics, as well as some recent physical models of biological evolution, and extreme value statistics.

physics.soc-ph↗
arXiv2006

Probability distribution of the maximum of a smooth temporal signal

We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a non-zero level M. When X(t) is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function, f(t)= .

cond-mat.stat-mech↗
arXiv2006

Distance traveled by random walkers before absorption in a random medium

We consider the penetration length $l$ of random walkers diffusing in a medium of perfect or imperfect absorbers of number density $ρ$. We solve this problem on a lattice and in the continuum in all dimensions $D$, by means of a mean-field renormalization group. For a homogeneous system in $D>2$, we find that $l\sim \max(ξ,ρ^{-1/2})$, where $ξ$ 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 $l$ in DLA clusters.

cond-mat.stat-mech↗
arXiv2006

Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t)\sim t^{1/z}, we find that for times t' and t satisfying L(t') << L(t) << L(t')^ϕwell inside the scaling regime, the spin autocorrelation function behaves like = L(t')^{-(d-2+η)} [L(t')/L(t)]^{λ_c}. For the O(n) model in the n -> \infty limit, we show that λ_c=d+2 and ϕ=z/2. We give a heuristic argument suggesting that this result is in fact valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.

cond-mat.stat-mech↗
arXiv2002

A precise approximation for directed percolation in d=1+1

We introduce an approximation specific to a continuous model for directed percolation, which is strictly equivalent to 1+1 dimensional directed bond percolation. We find that the critical exponent associated to the order parameter (percolation probability) is beta=(1-1/\sqrt{5})/2=0.276393202..., in remarkable agreement with the best current numerical estimate beta=0.276486(8).

cond-mat.stat-mech↗
arXiv2001

The spatial correlations in the velocities arising from a random distribution of point vortices

This paper is devoted to a statistical analysis of the velocity fluctuations arising from a random distribution of point vortices in two-dimensional turbulence. Exact results are derived for the correlations in the velocities occurring at two points separated by an arbitrary distance. We find that the spatial correlation function decays extremely slowly with the distance. We discuss the analogy with the statistics of the gravitational field in stellar systems.

cond-mat.stat-mech↗
arXiv2001

Random Fibonacci Sequences

Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1} decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently small (large) B. In the limits B --> 0 and B --> infinity, we expand the Lyapunov exponent lambda(B) in powers of B and B^{-1}, respectively. For the classical case of $β=1$ we obtain exact non-perturbative results. In particular, an invariant measure associated with Ricatti variable r_n=x_{n+1}/x_{n} is shown to exhibit plateaux around all rational.

cond-mat.stat-mech↗
arXiv2000

Ballistic Annihilation

Ballistic annihilation with continuous initial velocity distributions is investigated in the framework of Boltzmann equation. The particle density and the rms velocity decay as $c=t^{-α}$ and $ =t^{-β}$, with the exponents depending on the initial velocity distribution and the spatial dimension. For instance, in one dimension for the uniform initial velocity distribution we find $β=0.230472...$. We also solve the Boltzmann equation for Maxwell particles and very hard particles in arbitrary spatial dimension. These solvable cases provide bounds for the decay exponents of the hard sphere gas.

cond-mat.stat-mech↗
arXiv2000

Scaling laws and vortex profiles in 2D decaying turbulence

We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A self-similar scaling regime is detected when the scaling laws are expressed in units of mean vorticity and integral scale, as predicted by Carnevale et al., and it is observed that viscous effects spoil this scaling regime. This scaling regime shows some trends toward that of the Kirchhoff model, for which a recent theory predicts a decay exponent $ξ=1$. In terms of scaled variables, the vortices have a similar profile close to a Fermi-Dirac distribution.

cond-mat.stat-mech↗
arXiv2000

Numerical renormalization group of vortex aggregation in 2D decaying turbulence: the role of three-body interactions

In this paper, we introduce a numerical renormalization group procedure which permits long-time simulations of vortex dynamics and coalescence in a 2D turbulent decaying fluid. The number of vortices decreases as $N\sim t^{-ξ}$, with $ξ\approx 1$ instead of the value $ξ=4/3$ predicted by a na\"ıve kinetic theory. For short time, we find an effective exponent $ξ\approx 0.7$ consistent with previous simulations and experiments. We show that the mean square displacement of surviving vortices grows as $ \sim t^{1+ξ/2}$. Introducing effective dynamics for two-body and three-body collisions, we justify that only the latter become relevant at small vortex area coverage. A kinetic theory consistent with this mechanism leads to $ξ=1$. We find that the theoretical relations between kinetic parameters are all in good agreement with experiments.

cond-mat.stat-mech↗
arXiv2000

The statistics of velocity fluctuations arising from a random distribution of point vortices: the speed of fluctuations and the diffusion coefficient

This paper is devoted to a statistical analysis of the fluctuations of velocity and acceleration produced by a random distribution of point vortices in two-dimensional turbulence. We show that the velocity probability density function (p.d.f.) behaves in a manner which is intermediate between Gaussian and Lévy laws while the distribution of accelerations is governed by a Cauchy law. Our study accounts properly for a spectrum of circulations among the vortices. In the case of real vortices (with a finite core) we show analytically that the distribution of accelerations makes a smooth transition from Cauchy (for small fluctuations) to Gaussian (for large fluctuations) passing probably through an exponential tail. We introduce a function $T(V)$ which gives the typical duration of a velocity fluctuation $V$; we show that $T(V)$ behaves like $V$ and $V^{-1}$ for weak and large velocities respectively. These results have a simple physical interpretation in the nearest neighbor approximation and in Smoluchowski theory concerning the persistence of fluctuations. We discuss the analogies with respect to the fluctuations of the gravitational field in stellar systems. As an application of these results, we determine an approximate expression for the diffusion coefficient of point vortices. When applied to the context of freely decaying two-dimensional turbulence, the diffusion becomes anomalous and we establish a relationship $ν=1+{ξ\over 2}$ between the exponent of anomalous diffusion $ν$ and the exponent $ξ$ which characterizes the decay of the vortex density. This relation is in good agreement with laboratory experiments and numerical simulations.

cond-mat.stat-mech↗
arXiv1996

Analytical Results for Nontrivial Polydispersity Exponents in Aggregation Models

We study a Smoluchowski equation describing a simple mean-field model of particles moving in $d$ dimensions and aggregating with conservation of `mass' $s=R^D$ ($R$ is the particle radius). In the scaling regime the scaled mass distribution $P(s)\sim s^{-τ}$, and $τ$ can be computed by perturbative and non perturbative expansions. A possible application to two-dimensional decaying turbulence is briefly discussed.

cond-mat↗