Dario Villamaina

Université Paris-Sud 11, Orsay, Île-de-France, France

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Publications (23)34.81 Total impact

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    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, velocity-velocity correlations of the moving wall present a complex two-time relaxation that cannot be reproduced by a standard Langevin-like 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.
    Physical Review E 04/2014; 89(4-1):042105. · 2.31 Impact Factor
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    Gernot Akemann, Dario Villamaina, Pierpaolo Vivo
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    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 Sherrington-Kirkpatrick mean-field 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.
    Physical review. E, Statistical, nonlinear, and soft matter physics. 02/2014; 89(6-1).
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    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 heavy-tailed random matrices. We show that a central non-Gaussian 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 Tracy-Widom distribution known for Gaussian ensembles, both at small and large arguments and for any $\beta$. Our analytical results are confirmed by numerical simulations.
    Journal of Physics A Mathematical and Theoretical 10/2012; 46(2). · 1.77 Impact Factor
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    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 sub-diffusive 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.
    Physica Scripta 10/2012; 86(5):058516. · 1.03 Impact Factor
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    Dario Villamaina, Pierpaolo Vivo
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    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.
    Physical Review B 07/2012; 88(4). · 3.66 Impact Factor
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    A. Crisanti, A. Puglisi, D. Villamaina
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    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 fluctuation-dissipation theorem (FDT) are both related to the cross correlation between X1 and X2. Information about such cross correlation may be lost when single-variable 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.
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 06/2012; 85(6).
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    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).
    Journal of Statistical Mechanics Theory and Experiment 05/2012; 2012(06). · 1.87 Impact Factor
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    ABSTRACT: We discuss fluctuation-dissipation relations valid under general conditions even out of equilibrium. The response function is expressed in terms of unperperturbed correlation functions, where contributions peculiar to non-equilibrium 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.
    03/2012;
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    ABSTRACT: A massive intruder in a homogeneously driven granular fluid, in dilute configurations, performs a memory-less Brownian motion with drag and temperature simply related to the average density and temperature of the fluid. At volume fraction $\sim 10-50%$ 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 Fluctuation-Dissipation relation and the presence of a net entropy flux - from the fluid to the intruder - whose fluctuations satisfy the Fluctuation Relation.
    Granular Matter 01/2012; 14(2). · 1.50 Impact Factor
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    ABSTRACT: Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2D 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 Brownian-like 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 length-scales, 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 non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium 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. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales 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.
    The Journal of Chemical Physics 01/2012; 136(1):014704. · 3.12 Impact Factor
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    ABSTRACT: Velocity correlations in a quasi-2D driven granular fluid are studied in experiments and numerical simulations. The transverse velocity structure factor reveals two well-defined 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 non-equilibrium coherence length, growing with density, that characterizes order in the velocity field.
    EPL (Europhysics Letters) 09/2011; 96(1):14004. · 2.26 Impact Factor
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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 fluctuation-dissipation relation with the average granular temperature. Static velocity structure factors $S_\perp(k)$ and $S_\parallel(k)$ display a general non-constant 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.
    Journal of Statistical Mechanics Theory and Experiment 07/2011; 57. · 1.87 Impact Factor
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    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.
    American Journal of Physics 06/2011; 79. · 0.78 Impact Factor
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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 non-equilibrium coherence length $\xi$, growing with density, that characterizes order in the velocity field.
    03/2011;
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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 single-file, which are examples of systems with subdiffusive transport properties. The relevance of non-equilibrium 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.
    Journal of Statistical Mechanics Theory and Experiment 01/2011; 2011(01). · 1.87 Impact Factor
  • American Journal of Physics 01/2011; 79:980-980. · 0.78 Impact Factor
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    ABSTRACT: We study the dynamics of an asymmetric intruder in a glass-former model. At equilibrium, the intruder diffuses with average zero velocity. After an abrupt quench to T deeply under the mode-coupling temperature, a net average drift is observed, steady on a logarithmic time scale. The phenomenon is well reproduced in an asymmetric version of the Sinai model. The sub-velocity of the intruder grows with Teff/T, where Teff is defined by the response–correlation ratio, corresponding to a general behavior of thermal ratchets when in contact with two thermal reservoirs.
    Journal of Statistical Mechanics Theory and Experiment 12/2010; 2010(12):L12002. · 1.87 Impact Factor
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    ABSTRACT: A Generalized Langevin Equation with exponential memory is proposed for the dynamics of a massive intruder in a dense granular fluid. The model reproduces numerical correlation and response functions, violating the Equilibrium Fluctuation-Dissipation Relations. The source of memory is identified in the coupling of the tracer velocity V with a spontaneous local velocity field U in the surrounding fluid: fluctuations of this field introduce a new time scale with its associated length scale. Such identification allows us to measure the intruder's fluctuating entropy production as a function of V and U, obtaining a neat verification of the fluctuation relation.
    EPL (Europhysics Letters) 11/2010; 92(3):34001. · 2.26 Impact Factor
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    ABSTRACT: We study the dynamics of an asymmetric intruder in a glass-former model. At equilibrium, the intruder diffuses with average zero velocity. After an abrupt quench to T deeply under the modecoupling temperature, a neat average drift is observed, steady on a logarithmic time-scale. The phenomenon is well reproduced in an asymmetric version of the Sinai model. The subvelocity of the intruder grows with (T_{eff} - T)/T, where T_{eff} is defined by the response-correlation ratio, and corresponds to the general behavior of thermal ratchets when in contact with two thermal reservoirs. Comment: 4 pages, 4 figures
    07/2010;
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    ABSTRACT: We study the stochastic motion of an intruder in a dilute driven granular gas. All particles are coupled to a thermostat, representing the external energy source, which is the sum of random forces and a viscous drag. The dynamics of the intruder, in the large mass limit, is well described by a linear Langevin equation, combining the effects of the external bath and of the 'granular bath'. The drag and diffusion coefficients are calculated under a few assumptions, whose validity is well verified in numerical simulations. We also discuss the non-equilibrium properties of the intruder dynamics, as well as the corrections due to finite packing fraction or finite intruder mass.
    Journal of Statistical Mechanics Theory and Experiment 04/2010; 2010(04):P04013. · 1.87 Impact Factor