Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current Q _t during time t through the origin when, in the initial condition, the sites are occupied with density ρ _a on the negative axis and with density ρ _b on the positive axis. All the cumulants of Q _t grow like . In the range where , the decay exp [−Q _t ³/t] of the distribution of Q _t is non-Gaussian. Our results are obtained using the Bethe ansatz and several identities derived recently by Tracy and Widom for exclusion processes on the infinite line. We acknowledge the support of the French Ministry of Education through the ANR BLAN07-2184264 grant.     

Density and Correlations in Large One and Three Dimensional Systems of Fermions

The density and correlations are studied for a system of fermions moving in an average harmonic oscillator potential in one and three dimensions when the number of fermions are large. The technique is based on the use of Mehler's formula for the product of two Hermite functions and con-. tour integrations. Wigner transform is then calculated using this technique. It is shown that it becomes a step function when number of fermions become large. By integrating out momenta, an expression for the density of fermions is derived. Two-particle correlation function is studied in detail. Dyson's type of correlations for a system of nucleons is studied. The connection between one dimensional system of fermions and eigenvalues of a random Hermitean Hamiltonian is shown. The Coulomb energy difference of isobars is studied using nucleon density and correlations.     

Flux Fluctuations in the One Dimensional Nearest Neighbors Symmetric Simple Exclusion Process

Let J(t) be the the integrated flux of particles in the symmetric simple exclusion process starting with the product invariant measure ν _ρ with density ρ. We compute its rescaled asymptotic variance: $$\mathop {\lim }\limits_{t \to \infty } t^{ - 1/2} \mathbb{V}J(t) = \sqrt {2/\pi } (1 - \rho )\rho$$ Furthermore we show that t ^?1/4 J(t) converges weakly to a centered normal random variable with this variance. From these results we compute the asymptotic variance of a tagged particle in the nearest neighbor case and show the corresponding central limit theorem.     

Advances of Reflectometry on Tore-Supra: From Edge Density Profile to Core Density Fluctuations

A new generation of broadband reflectometers based on solid state components has been installed on Tore-Supra. With reflectometers covering the range 50 to 155 GHz, the whole plasma can be scanned. Two X-mode reflectometers (V and W band) are dedicated to electron density profile measurements. Diagnostics are operated routinely with an automatic algorithm to reconstruct the density profile from shot to shot. A fast acquisition mode is available to study short time plasma evolution. For turbulence and transport studies, a third reflectometer operating between 105 and 155 GHz measures density fluctuations in the plasma centre. Sensitive to large scales, it can retrieve density perturbation due to MHD modes or broadband turbulence. Lastly, a Doppler reflectometer, based on back scattering, is being installed for measuring the poloidal rotation and fluctuations amplitude at higher wave numbers.     

Step Fluctuations for a Faceted Crystal

A statistical mechanics model for a faceted crystal is the 3D Ising model at zero temperature. It is assumed that in one octant all sites are occupied by atoms, the remaining ones being empty. Allowed atom configurations are such that they can be obtained from the filled octant through successive removals of atoms with breaking of precisely three bonds. If V denotes the number of atoms removed, then the grand canonical Boltzmann weight is q ^V , 0<q<1. As shown by Cerf and Kenyon, in the limit q1 a deterministic shape is attained, which has the three facets (100), (010), (001), and a rounded piece interpolating between them. We analyse the step statistics as q1. In the rounded piece it is given by a determinantal process based on the discrete sine-kernel. Exactly at the facet edge, the steps have more space to meander. Their statistics is again determinantal, but this time based on the Airy-kernel. In particular, the border step is well approximated by the Airy process, which has been obtained previously in the context of growth models. Our results are based on the asymptotic analysis for space-time inhomogeneous transfer matrices.     

Current Density Profile Measurements in the Proto-Cleo Torsatron

Current density profile measurements were obtained in the Proto-Cleo torsatron (R = 40 cm, a = 5 cm, I = 3, BT = 3 kG, n? ~ 1011 cm-3, Te ~ 20 eV) by using a small back-to-back flat double probe. Three different operating circuits used with this probe are presented, along with experimental results, all showing good agreement. Current is seen to flow only within the separatrix, in channels which follow the magnetic surfaces as they move radially inward with time due to changing vertical magnetic flux.     

Asymptotics in ASEP with Step Initial Condition

In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use this formula to obtain three asymptotic results for the positions of these particles. In one an apparently new distribution function arises and in another the distribution function F ₂ arises. The latter extends a result of Johansson on TASEP to ASEP, and hence proves KPZ universality for ASEP with step initial condition.     

低速二维后向台阶流动中的壁面压强脉动

为了能排除三维结构对涡脱和剪切层旋涡的影响,使用实验方法研究了一个小展高比（AR=0.125）的后向台阶流动.该实验台类似纯二维的Hele-Shaw Cell.流动被局限在两个平行且距离为5 mm的有机玻璃板之间.台阶高度H为40 mm,扩张比2:3.在台阶下游中央沿流动方向安装16个麦克风组成的传感器阵列采集壁面脉动压强.来流速度U₀在9~26 m/s之间连续可调.通过计算脉动压强分布、频谱,不同位置的相关性和相干性系数,发现并分析流动存在一个临界Reynolds数.流场在临界Reynolds数前后存在明显不同的流动特征.实验结果表明在低Reynolds数下依然存在剪切层的低频摆动;当Reynolds数大于临界Reynolds数时,分离后流动由涡结构传播的特性主导.      

Cusp Singularities in Boundary-Driven Diffusive Systems

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be non-differentiable, a phenomenon that is unique to non-equilibrium systems, and discuss the types of models which display such singularities. The structure of these singularities is found to generically be a cusp, which can be described by a Landau free energy or, equivalently, by catastrophe theory. Connections with analogous results in systems with finite-dimensional phase spaces are drawn.     

On ASEP with Step Bernoulli Initial Condition

This paper extends earlier work on ASEP to the case of step Bernoulli initial condition. The main results are a representation in terms of a Fredholm determinant for the probability distribution of a fixed particle, and asymptotic results which in particular establish KPZ universality for this probability in one regime. (And, as a corollary, for the current fluctuations.)     

Current Fluctuations in a Semiconductor Quantum Dot with Large Energy Spacing

Current fluctuation in electronic systems has been extensively studied due to the fact that they can pro- vide further information of charge transport compared to the conventional conductance measurements. Shot noise is the non-equilibrium electrical fluctuation due to the discrete nature of carriers flowing through a device, reflecting correlation effects. A well-known shot noise power density as uncorrelated charge trans- mission is S - 2el, with I the average current. This Poissonian shot noise can be observed in sys- tems with a single tunnel barrier. Positive or neg- ative correlations between charged particles, induced by the Coulomb interaction and the Pauli exclusion principle, can enhance or suppress shot noise from the Poissonian value. Numerous experimental and the- oretical studies of the shot noise in mesoseopie sys- tems have been carried out on various devices such as self-assembled quantum dots, resonant tunnel- ing diodes,molecular junction devices, quan- tum point contacts,semiconductor quantum dots, and metal atomic chains. Externally driven exci- tations which affect shot noise properties were also investigated.     

Coherent Stochastic Resonance in One Dimensional Diffusion with One Reflecting and One Absorbing Boundaries

It is shown that the single-step periodic signal (periodic telegraph signal) can not produce coherent stochastic resonance for diffusion on a segment with one absorbing and one reflecting end points while the multi-step periodic signal does. The general features of this process are exihibited. The resonant frequency is found to decrease and the mean first passage time at resonant frequency increases linearly, as we increase the length of the medium. The cycle variable is shown to be the proper argument to express the first passage probability at resonance. A formula for first passage probability at resonance is derived in terms of two universal functions, which clearly isolates its dependence on the length of the medium.     

Energy Profile Fluctuations in Dissipative Nonequilibrium Stationary States

The exact large deviation function (ldf) for the fluctuations of the energy density field is computed for a chain of Ising (or more generally Potts) spins driven by a zero-temperature (dissipative) Glauber dynamics and sustained in a nontrivial stationary regime by an arbitrary energy injection mechanism at the boundary of the system. It is found that this ldf is independent of the dynamical details of the energy injection, and that the energy fluctuations, unlike conservative systems in a nonequilibrium state, are not spatially correlated in the stationary regime.This revised version was published online in March 2005 with corrections to the page numbers.     

Step Density Profiles in Localized Chains

We consider two types of strongly disordered one-dimensional Hamiltonian systems coupled to baths (energy or particle reservoirs) at the boundaries: strongly disordered quantum spin chains and disordered classical harmonic oscillators. These systems are believed to exhibit localization, implying in particular that the conductivity decays exponentially in the chain length L. We ask however for the profile of the (very slowly) transported quantity in the steady state. We find that this profile is a step-function, jumping in the middle of the chain from the value set by the left bath to the value set by the right bath. This is confirmed by numerics on a disordered quantum spin chain of 9 spins and on much longer chains of harmonic oscillators. From theoretical arguments, we find that the width of the step grows not faster than \(\sqrt{L}\), and we confirm this numerically for harmonic oscillators. In this case, we also observe a drastic breakdown of local equilibrium at the step, resulting in a heavily oscillating temperature profile.     

Charge Fluctuations in Finite Coulomb Systems

When described in a grand canonical ensemble, a finite Coulomb system exhibits charge fluctuations. These fluctuations are studied in the case of a classical (i.e., non-quantum) system with no macroscopic average charge. Assuming the validity of macroscopic electrostatics gives, on a three-dimensional finite large conductor of volume V, a mean square charge Q ² which goes as V ^1/3. More generally, in a short-circuited capacitor of capacitance C, made of two conductors, the mean square charge on one conductor is Q ²=TC, where T is the temperature and C the capacitance of the capacitor. The case of only one conductor in a grand canonical ensemble is obtained by removing the other conductor to infinity. The general formula is checked in the weak-coupling (Debye–Hückel) limit for a spherical capacitor. For two-dimensional Coulomb systems (with logarithmic interactions), there are exactly solvable models which reveal that, in some cases, macroscopic electrostatics is not applicable even for large conductors. This is when the charge fluctuations involve only a small number of particles. The mean square charge on one two-dimensional system alone, in the grand canonical ensemble, is expected to be, at most, one squared elementary charge.     

Field Theory of Critical Behavior in Driven Diffusive Systems with Quenched Disorder

We present a field-theoretic renormalization-group study for the critical behavior of a uniformly driven diffusive system with quenched disorder, which is modeled by different kinds of potential barriers between sites. Due to their symmetry properties, these different realizations of the random potential barriers lead to three different models for the phase transition to transverse order and to one model for the phase transition to longitudinal order all belonging to distinct universality classes. In these four models, which have different upper critical dimensions d _c, we find the critical scaling behavior of the vertex functions in spatial dimensions d<d _c. The deviation from purely diffusive behavior is characterized by the anomaly exponent , which we calculate at first and second order, respectively, in =d _c–d. In each model turns out to be positive, which means superdiffusive spread of density fluctuations in the driving force direction.     

Exponential Clogging Time for a One Dimensional DLA

In this paper a simple DLA type model is analyzed. In (Benjamini and Yadin in Commun. Math. Phys. 279:187–223, [2008]) the standard DLA model from (Witten and Sander in Phys. Rev. B 27:5686–5697, [1983]) was considered on a cylinder and the arm growing phenomena was established, provided that the section of the cylinder has sufficiently fast mixing rate. When considering DLA on a cylinder it is natural to ask how many particles it takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we formulate a very simple DLA clogging model and establish an exponential lower bound on the number of particles arriving before clogging appears. In particular we possibly shed some light on why it takes so long to reach the bypass operation.     

Travelling with/against the Flow. Deterministic Diffusive Driven Systems

We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars moving in opposite directions along a narrow road. Our main results concern the Fundamental diagram of the system describing the dependence of average particle velocities on their densities and the Phase diagram describing the partition of the space of particle configurations into regions having different qualitative properties, which we identify with free, jammed and hysteresis phases. This research has been partially supported by Russian Foundation for Fundamental Research, CRDF and French Ministry of Education grants.