Publications (28)52.57 Total impact

Article: Blast Dynamics in a Dissipative Gas
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ABSTRACT: The blast caused by an intense explosion has been extensively studied in conservative fluids, where the Taylorvon NeumannSedov hydrodynamic solution is a prototypical example of selfsimilarity driven by conservation laws. In dissipative media however, energy conservation is violated, yet a distinctive selfsimilar solution appears. It hinges on the decoupling of random and coherent motion permitted by a broad class of dissipative mechanisms. This enforces a peculiar layered structure in the shock, for which we derive the full hydrodynamic solution, validated by a microscopic approach based on Molecular Dynamics simulations. We predict and evidence a succession of temporal regimes, as well as a longtime corrugation instability, also selfsimilar, which disrupts the blast boundary. These generic results may apply from astrophysical systems to granular gases, and invite further crossfertilization between microscopic and hydrodynamic approaches of shockwaves.  [Show abstract] [Hide abstract]
ABSTRACT: We study the behavior of a moving wall in contact with a particle gas and subjected to an external force. We compare the fluctuations of the system observed in the microcanonical and canonical ensembles, by varying the number of particles. Static and dynamic correlations signal significant differences between the two ensembles. Furthermore, velocityvelocity correlations of the moving wall present a complex twotime relaxation that cannot be reproduced by a standard Langevinlike description. Quite remarkably, increasing the number of gas particles in an elongated geometry, we find a typical time scale, related to the interaction between the partitioning wall and the particles, which grows macroscopically.  [Show abstract] [Hide abstract]
ABSTRACT: We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the loop equation with the additional constraint of vanishing trace on average. The density is generally supported on two disconnected intervals lying on the two sides of the pole. In the limit of having no pole, we recover the standard semicircle. Obtained in the planar limit, our results apply to matrices with orthogonal, unitary or symplectic symmetry alike. The orthogonal case with $m=2$ is motivated by an application to spin glass physics. In the SherringtonKirkpatrick meanfield model, in the paramagnetic phase and for sufficiently large systems the spin glass susceptibility is a random variable, depending on the realization of disorder. It is essentially given by a linear statistics on the eigenvalues of the coupling matrix. As such its large deviation function can be computed using standard Coulomb fluid techniques. The resulting free energy of the associated fluid precisely corresponds to the partition function of our random matrix model. Numerical simulations provide an excellent confirmation of our analytical results.  [Show abstract] [Hide abstract]
ABSTRACT: The isothermal compressibility of an interacting or non interacting system may be extracted from the fluctuations of the number of particles in a well chosen control volume. Finite size effects are prevalent and should then be accounted for to obtain a meaningful, thermodynamic compressibility. In the traditional computational setup where a given simulation box is replicated with periodic boundary conditions, we study particle number fluctuations outside the box (i.e. when the control volume exceeds the box itself), which bear relevant thermodynamic information. We also investigate the related problem of extracting the compressibility from the structure factor in the small wavevector limit ($k\to 0$). The calculation should be restricted to the discrete set of wavevectors $k$ that are compatible with the periodicity of the system, and we assess the consequences of considering other $k$ values, a widespread error among beginners. 
Article: Large deviations of Brownian motors
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ABSTRACT: We review some recent results on the behavior of fluctuations in the framework of molecular motors. We present both theoretical and experimental studies, pointing out some interesting analogies shown by the large deviations of quantities such as work and entropy production in different systems. These common features reveal some underlying symmetry properties governing the nonequilibrium behavior of Brownian motors.  [Show abstract] [Hide abstract]
ABSTRACT: We discuss the role of nonequilibrium conditions in the context of anomalous dynamics. We study in detail the response properties in different models, featuring subdiffusion and superdiffusion: in such models, the presence of currents induces a violation of the Einstein relation. We show how in some of them it is possible to find the correlation function proportional to the linear response, in other words, we have a generalized fluctuationresponse relation.  [Show abstract] [Hide abstract]
ABSTRACT: We compute analytically the probability density function (pdf) of the largest eigenvalue $\lambda_{\max}$ in rotationally invariant Cauchy ensembles of $N\times N$ matrices. We consider unitary ($\beta = 2$), orthogonal ($\beta =1$) and symplectic ($\beta=4$) ensembles of such heavytailed random matrices. We show that a central nonGaussian regime for $\lambda_{\max} \sim \mathcal{O}(N)$ is flanked by large deviation tails on both sides which we compute here exactly for any value of $\beta$. By matching these tails with the central regime, we obtain the exact leading asymptotic behaviors of the pdf in the central regime, which generalizes the TracyWidom distribution known for Gaussian ensembles, both at small and large arguments and for any $\beta$. Our analytical results are confirmed by numerical simulations.  [Show abstract] [Hide abstract]
ABSTRACT: We study the Einstein relation between spontaneous fluctuations and the response to an external perturbation for the comb model and the single file, which are examples of systems with subdiffusive transport properties. The relevance of nonequilibrium conditions is investigated: when a stationary current (in the form of a drift or an energy flux) is present, the Einstein relation breaks down. In the case of the comb model, a general relation—appearing in the recent literature—between the response function and an unperturbed suitable correlation function allows us to explain the obtained results. This suggests that the relevant ingredient in breaking the Einstein formula, for stationary regimes, is not anomalous diffusion but the presence of currents driving the system out of equilibrium.  [Show abstract] [Hide abstract]
ABSTRACT: We compute analytically the distributions of concurrence $\bm{\mathcal{C}}$ and squared norm $\bm{\mathcal{N}}$ for the production of electronic entanglement in a chaotic quantum dot. The dot is connected to the external world via one ideal and one partially transparent lead, characterized by the opacity $\gamma$. The average concurrence increases with $\gamma$ while the average squared norm of the entangled state decreases, making it less likely to be detected. When a minimal detectable norm $\bm{\mathcal{N}}_0$ is required, the average concurrence is maximal for an optimal value of the opacity $\gamma^\star(\bm{\mathcal{N}}_0)$ which is explicitly computed as a function of $\bm{\mathcal{N}}_0$. If $\bm{\mathcal{N}}_0$ is larger than the critical value $\bm{\mathcal{N}}_0^\star\simeq 0.3693\dots$, the average entanglement production is maximal for the completely ideal case, a direct consequence of an interesting bifurcation effect.  [Show abstract] [Hide abstract]
ABSTRACT: We discuss the relevance of information contained in cross correlations among different degrees of freedom, which is crucial in nonequilibrium systems. In particular we consider a stochastic system where two degrees of freedom X1 and X2—in contact with two different thermostats—are coupled together. The production of entropy and the violation of equilibrium fluctuationdissipation theorem (FDT) are both related to the cross correlation between X1 and X2. Information about such cross correlation may be lost when singlevariable reduced models for X1 are considered. Two different procedures are typically applied: (a) one totally ignores the coupling with X2; and (b) one models the effect of X2 as an average memory effect, obtaining a generalized Langevin equation. In case (a) discrepancies between the system and the model appear both in entropy production and linear response; the latter can be exploited to define effective temperatures, but those are meaningful only when time scales are well separated. In case (b) linear response of the model well reproduces that of the system; however the loss of information is reflected in a loss of entropy production. When only linear forces are present, such a reduction is dramatic and makes the average entropy production vanish, posing problems in interpreting FDT violations.  [Show abstract] [Hide abstract]
ABSTRACT: We study the Einstein relation between diffusion and response to an external field in systems showing superdiffusion. In particular, we investigate a continuous time Levy walk where the velocity remains constant for a time \tau, with distribution P(\tau) \tau^{g}. At varying g the diffusion can be standard or anomalous; in spite of this, if in the unperturbed system a current is absent, the Einstein relation holds. In the case where a current is present the scenario is more complicated and the usual Einstein relation fails. This suggests that the main ingredient for the breaking of the Einstein relation is not the anomalous diffusion but the presence of a mean drift (current).  [Show abstract] [Hide abstract]
ABSTRACT: We discuss fluctuationdissipation relations valid under general conditions even out of equilibrium. The response function is expressed in terms of unperperturbed correlation functions, where contributions peculiar to nonequilibrium can appear. Such extra terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with two examples: driven granular systems and anomalous diffusion on comb structures.  [Show abstract] [Hide abstract]
ABSTRACT: A massive intruder in a homogeneously driven granular fluid, in dilute configurations, performs a memoryless Brownian motion with drag and temperature simply related to the average density and temperature of the fluid. At volume fraction $\sim 1050%$ the intruder's velocity correlates with the local fluid velocity field: such situation is approximately described by a system of coupled linear Langevin equations equivalent to a generalized Brownian motion with memory. Here one may verify the breakdown of the FluctuationDissipation relation and the presence of a net entropy flux  from the fluid to the intruder  whose fluctuations satisfy the Fluctuation Relation.  [Show abstract] [Hide abstract]
ABSTRACT: Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi2D fluidized granular experiment, with packing fractions φ ∈ [10%, 40%]. The fluidization is realized by vertically vibrating a rough plate, on top of which particles perform a Brownianlike horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large lengthscales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a nonequilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with nonequilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equaltime velocity structure factors display a peculiar shape with a plateau at large lengthscales and another one at small scales, marking two different temperatures: the "bath" temperature T(b), depending on shaking parameters, and the "granular" temperature T(g) < T(b), which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with φ, after proper rescaling with the mean free path.  [Show abstract] [Hide abstract]
ABSTRACT: Velocity correlations in a quasi2D driven granular fluid are studied in experiments and numerical simulations. The transverse velocity structure factor reveals two welldefined energy scales, associated with the external "bath temperature"Tb and with the internal granular one, Tg<Tb, relevant at large and small wavelengths, respectively. Experimental and numerical data are discussed within a fluctuating hydrodynamics model, which allows one to define and measure a nonequilibrium coherence length, growing with density, that characterizes order in the velocity field. 
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ABSTRACT: Static and dynamical structure factors for shear and longitudinal modes of the velocity and density fields are computed for a granular system fluidized by a stochastic bath with friction. Analytical expressions are obtained through fluctuating hydrodynamics and are successfully compared with numerical simulations up to a volume fraction $\sim 50%$. Hydrodynamic noise is the sum of external noise due to the bath and internal one due to collisions. Only the latter is assumed to satisfy the fluctuationdissipation relation with the average granular temperature. Static velocity structure factors $S_\perp(k)$ and $S_\parallel(k)$ display a general nonconstant behavior with two plateaux at large and small $k$, representing the granular temperature $T_g$ and the bath temperature $T_b>T_g$ respectively. From this behavior, two different velocity correlation lengths are measured, both increasing as the packing fraction is raised. This growth of spatial order is in agreement with the behaviour of dynamical structure factors, the decay of which becomes slower and slower at increasing density.  [Show abstract] [Hide abstract]
ABSTRACT: The energy of a finite system thermally connected to a thermal reservoir may fluctuate, while the temperature is a constant representing a thermodynamic property of the reservoir. The finite system can also be used as a thermometer for the reservoir. From such a perspective the temperature has an uncertainty, which can be treated within the framework of estimation theory. We review the main results of this theory, and clarify some controversial issues regarding temperature fluctuations. We also offer a simple example of a thermometer with a small number of particles. We discuss the relevance of the total observation time, which must be much longer than the decorrelation time. 
Article: Growing nonequilibrium length in granular fluids: from experiment to fluctuating hydrodynamics
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ABSTRACT: Velocity correlations in a 2D granular fluid are studied in experiments and numerical simulations. The transverse component of the velocity structure factor reveals two well defined energy scales, associated with the external "bath temperature" $T_b$ and with the internal granular one, $T_g<T_b$, relevant at large and small wavelengths respectively. Experimental and numerical data are discussed within a fluctuating hydrodynamics model, which allows one to define and measure a nonequilibrium coherence length $\xi$, growing with density, that characterizes order in the velocity field. 
Article: On anomalous diffusion and the out of equilibrium response function in onedimensional models
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ABSTRACT: We study how the Einstein relation between spontaneous fluctuations and the response to an external perturbation holds in the absence of currents, for the comb model and the elastic singlefile, which are examples of systems with subdiffusive transport properties. The relevance of nonequilibrium conditions is investigated: when a stationary current (in the form of a drift or an energy flux) is present, the Einstein relation breaks down, as is known to happen in systems with standard diffusion. In the case of the comb model, a general relation, which has appeared in the recent literature, between the response function and an unperturbed suitable correlation function, allows us to explain the observed results. This suggests that a relevant ingredient in breaking the Einstein formula, for stationary regimes, is not the anomalous diffusion but the presence of currents driving the system out of equilibrium.
Publication Stats
279  Citations  
52.57  Total Impact Points  
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Institutions

2015

French National Centre for Scientific Research
Lutetia Parisorum, ÎledeFrance, France


20122014

Université ParisSud 11
Orsay, ÎledeFrance, France


20082012

Sapienza University of Rome
 Department of Physics
Roma, Latium, Italy
