Alessandro Sarracino - Academia.edu (original) (raw)
Papers by Alessandro Sarracino
We study the dynamics of an asymmetric intruder in a glass-former model. At equilibrium, the intr... more 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 TTT 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 subvelocity of the
Comptes Rendus Physique, 2015
We review a few representative examples of granular experiments or models where phase separation,... more We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular media. Thereafter, dilute systems, the so-called "granular gases" are discussed: idealized kinetic models, such as the gas of inelastic hard spheres in the cooling regime, are the optimal playground to study the slow growth of correlated structures, e.g. shear patterns, vortices and clusters. In fluidized experiments, liquid-gas or solid-gas separations have been observed. In the case of monolayers of particles, phase coexistence and coarsening appear in several different setups, with mechanical or electrostatic energy input. Phenomenological models describe, even quantitatively, several experimental measures, both for the coarsening dynamics and for the dynamic transition between different granular phases. The origin of the underlying bistability is in general related to negative compressibility from granular hydrodynamics computations, even if the understanding of the mechanism is far from complete. A relevant problem, with important industrial applications, is related to the demixing or segregation of mixtures, for instance in rotating tumblers or on horizontally vibrated plates. Finally, the problem of compaction of highly dense granular materials, which has many important applications, is usually described in terms of coarsening dynamics: there, bubbles of mis-aligned grains evaporate, allowing the coalescence of optimally arranged islands and a progressive reduction of total occupied volume.
ABSTRACT We consider a broad class of Continuous Time Random Walks with large fluctuations effect... more ABSTRACT We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.
ABSTRACT We study the dynamics of an asymmetric intruder in a glass-former model. At equilibrium,... more 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
Journal of Physics a-Mathematical and Theoretical, 2013
We study the fluctuations of a stochastic Maxwell-Lorentz particle model driven by an external fi... more We study the fluctuations of a stochastic Maxwell-Lorentz particle model driven by an external field to determine the extent to which fluctuation relations are related to large deviations. Focusing on the total entropy production of this model in its steady state, we show that, although the probability density of this quantity globally satisfies (by definition) a fluctuation relation, its negative tail decays exponentially with time, whereas its positive tail decays slower than exponentially with time because of long collision-free trajectories. This provides an example of physical system for which the fluctuation relation does not derive, as commonly thought, from a probability density decaying everywhere exponentially with time or, in other words, from a probability density having a uniform large deviation form.
Physical Review Letters, 2014
We study the behavior of the stationary velocity of a driven particle in an environment of mobile... more We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.
Traffic and Granular Flow’05, 2007
We review recent results about the segregation process of a granular mixture of disks on an horiz... more We review recent results about the segregation process of a granular mixture of disks on an horizontally oscillating tray. In this condition an initially disordered mixture first segregates via the formation of stripes perpendicular to the driving direction; then stripes merge in a coarsening process. We discuss quantitatively both the short-time and the long-time dynamics of the system, and the dependence of the observed phenomenology on the frequency and amplitude of oscillation of the tray. The same system is also investigated when, instead of being disordered, is initially prepared in two stripes parallel to the driving direction. In this condition the interface between the two stripes manifests an instability which again leads to the formation of stripes perpendicular to the driving direction. Finally, we shortly review the mechanism which have been proposed in order to explain the observed segregation process.
Communications in Theoretical Physics, 2014
Lecture Notes in Physics, 2014
Physical Review E, 2014
We study the behavior of a moving wall in contact with a particle gas and subjected to an externa... more 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.
PLoS ONE, 2014
The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as foun... more The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own "effective" temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein's relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased.
Physical Review Letters, 2014
We use a relationship between response and correlation function in nonequilibrium systems to esta... more We use a relationship between response and correlation function in nonequilibrium systems to establish a connection between the heat production and the deviations from the equilibrium fluctuation-dissipation theorem. This scheme extends the Harada-Sasa formulation [Phys. Rev. Lett. 95, 130602 (2005)], obtained for Langevin equations in steady states, as it also holds for transient regimes and for discrete jump processes involving small entropic changes. Moreover, a general formulation includes two times and the new concepts of two-time work, kinetic energy, and of a two-time heat exchange that can be related to a nonequilibrium "effective temperature". Numerical simulations of a chain of anharmonic oscillators and of a model for a molecular motor driven by ATP hydrolysis illustrate these points.
Physical Review Letters, 2013
The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtaine... more The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical non-equilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a net drift induced by friction. If the thermal bath is replaced by a granular gas, the well known granular ratchet effect also intervenes, becoming dominant at high collision rates. For our chosen wheel shape the granular effect acts in the opposite direction with respect to the frictioninduced torque, resulting in the inversion of the ratchet direction as the collision rate increases. We have realized a new granular ratchet experiment where both these ratchet effects are observed, as well as the predicted inversion at their crossover. Our discovery paves the way to the realization of micro and sub-micrometer Brownian motors in an equilibrium fluid, based purely upon nano-friction.
Physical Review E, 2008
A unified derivation of the off equilibrium fluctuation dissipation relations (FDR) is given for ... more A unified derivation of the off equilibrium fluctuation dissipation relations (FDR) is given for Ising and continous spins to arbitrary order, within the framework of Markovian stochastic dynamics. Knowledge of the FDR allows to develop zero field algorithms for the efficient numerical computation of the response functions. Two applications are presented. In the first one, the problem of probing for the existence of a growing cooperative length scale is considered in those cases, like in glassy systems, where the linear FDR is of no use. The effectiveness of an appropriate second order FDR is illustrated in the test case of the Edwards-Anderson spin glass in one and two dimensions. In the second one, the important problem of the definition of an off equilibrium effective temperature through the nonlinear FDR is considered. It is shown that, in the case of coarsening systems, the effective temperature derived from the second order FDR is consistent with the one obtained from the linear FDR. †lippiello@sa.infn.it ‡corberi@sa.infn.it ¶sarracino@sa.infn.it §zannetti@sa.infn.it PACS: 05.70.Ln, 75.40.Gb,
Physical Review E, 2013
The effect of Coulomb friction is studied in the framework of collisional ratchets. It turns out ... more The effect of Coulomb friction is studied in the framework of collisional ratchets. It turns out that the average drift of these devices can be expressed as the combination of a term related to the lack of equipartition between the probe and the surrounding bath, and a term featuring the average frictional force. We illustrate this general result in the asymmetric Rayleigh piston, showing how Coulomb friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath. An explicit analytical expression for the average velocity of the piston is obtained in the rare collision limit. Numerical simulations support the analytical findings.
Physical Review E, 2013
We report the study of an experimental granular Brownian motor, inspired by the one published in ... more We report the study of an experimental granular Brownian motor, inspired by the one published in Eshuis et al. [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating blade, the surfaces of which break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main difference of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance v(0)(2). We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions, with an average angular velocity <ω>~v(0)(3), and (ii) frequent collisions (FC), with <ω>~v(0). We also study the fluctuations of the angle spanned in a large-time interval Δθ, which in the FC regime is proportional to the work done upon the motor. We observe that the fluctuation relation is satisfied with a slope which weakly depends on the relative collision frequency.
Physical Review E, 2010
We discuss the relation between the fluctuation-dissipation relation derived by Chatelain and Ric... more We discuss the relation between the fluctuation-dissipation relation derived by Chatelain and Ricci-Tersenghi [C.Chatelain, J.Phys. A 36, 10739 (2003); F. Ricci-Tersenghi, Phys.Rev.E 68, 065104(R) (2003)] and that by Lippiello-Corberi-Zannetti [E. Lippiello, F. Corberi and M. Zannetti Phys. Rev. E 71, 036104 (2005)]. In order to do that, we re-derive the fluctuation-dissipation relation for systems of discrete variables evolving in discrete time via a stochastic non-equilibrium Markov process. The calculation is carried out in a general formalism comprising the Chatelain, Ricci-Tersenghi result and that by Lippiello-Corberi-Zannetti as special cases. The applicability, generality, and experimental feasibility of the two approaches is thoroughly discussed. Extending the analytical calculation to the variance of the response function we show the vantage of field-free numerical methods with respect to the standard method where the perturbation is applied. We also show that the signal to noise ratio is better (by a factor √ 2) in the algorithm of Lippiello-Corberi-Zannetti with respect to that of Chatelain-Ricci Tersenghi. PACS: 05.70.Ln, 75.40.Gb, 05.40.-a I. INTRODUCTION
Physical Review B, 2008
We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a ... more We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a generic observable to the appropriate correlation functions, for Markov systems. The relation, which takes a similar form for systems governed by a master equation or by a Langevin equation, can be derived to every order, in large generality with respect to the considered model, in equilibrium and out of equilibrium as well. On the basis of the fluctuation dissipation relation we propose a particular response function, namely the second order susceptibility of the two-particle correlation function, as an effective quantity to detect and quantify cooperative effects in glasses and disordered systems. We test this idea by numerical simulations of the Edwards-Anderson model in one and two dimensions.
We study the dynamics of an asymmetric intruder in a glass-former model. At equilibrium, the intr... more 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 TTT 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 subvelocity of the
Comptes Rendus Physique, 2015
We review a few representative examples of granular experiments or models where phase separation,... more We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular media. Thereafter, dilute systems, the so-called "granular gases" are discussed: idealized kinetic models, such as the gas of inelastic hard spheres in the cooling regime, are the optimal playground to study the slow growth of correlated structures, e.g. shear patterns, vortices and clusters. In fluidized experiments, liquid-gas or solid-gas separations have been observed. In the case of monolayers of particles, phase coexistence and coarsening appear in several different setups, with mechanical or electrostatic energy input. Phenomenological models describe, even quantitatively, several experimental measures, both for the coarsening dynamics and for the dynamic transition between different granular phases. The origin of the underlying bistability is in general related to negative compressibility from granular hydrodynamics computations, even if the understanding of the mechanism is far from complete. A relevant problem, with important industrial applications, is related to the demixing or segregation of mixtures, for instance in rotating tumblers or on horizontally vibrated plates. Finally, the problem of compaction of highly dense granular materials, which has many important applications, is usually described in terms of coarsening dynamics: there, bubbles of mis-aligned grains evaporate, allowing the coalescence of optimally arranged islands and a progressive reduction of total occupied volume.
ABSTRACT We consider a broad class of Continuous Time Random Walks with large fluctuations effect... more ABSTRACT We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.
ABSTRACT We study the dynamics of an asymmetric intruder in a glass-former model. At equilibrium,... more 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
Journal of Physics a-Mathematical and Theoretical, 2013
We study the fluctuations of a stochastic Maxwell-Lorentz particle model driven by an external fi... more We study the fluctuations of a stochastic Maxwell-Lorentz particle model driven by an external field to determine the extent to which fluctuation relations are related to large deviations. Focusing on the total entropy production of this model in its steady state, we show that, although the probability density of this quantity globally satisfies (by definition) a fluctuation relation, its negative tail decays exponentially with time, whereas its positive tail decays slower than exponentially with time because of long collision-free trajectories. This provides an example of physical system for which the fluctuation relation does not derive, as commonly thought, from a probability density decaying everywhere exponentially with time or, in other words, from a probability density having a uniform large deviation form.
Physical Review Letters, 2014
We study the behavior of the stationary velocity of a driven particle in an environment of mobile... more We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.
Traffic and Granular Flow’05, 2007
We review recent results about the segregation process of a granular mixture of disks on an horiz... more We review recent results about the segregation process of a granular mixture of disks on an horizontally oscillating tray. In this condition an initially disordered mixture first segregates via the formation of stripes perpendicular to the driving direction; then stripes merge in a coarsening process. We discuss quantitatively both the short-time and the long-time dynamics of the system, and the dependence of the observed phenomenology on the frequency and amplitude of oscillation of the tray. The same system is also investigated when, instead of being disordered, is initially prepared in two stripes parallel to the driving direction. In this condition the interface between the two stripes manifests an instability which again leads to the formation of stripes perpendicular to the driving direction. Finally, we shortly review the mechanism which have been proposed in order to explain the observed segregation process.
Communications in Theoretical Physics, 2014
Lecture Notes in Physics, 2014
Physical Review E, 2014
We study the behavior of a moving wall in contact with a particle gas and subjected to an externa... more 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.
PLoS ONE, 2014
The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as foun... more The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own "effective" temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein's relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased.
Physical Review Letters, 2014
We use a relationship between response and correlation function in nonequilibrium systems to esta... more We use a relationship between response and correlation function in nonequilibrium systems to establish a connection between the heat production and the deviations from the equilibrium fluctuation-dissipation theorem. This scheme extends the Harada-Sasa formulation [Phys. Rev. Lett. 95, 130602 (2005)], obtained for Langevin equations in steady states, as it also holds for transient regimes and for discrete jump processes involving small entropic changes. Moreover, a general formulation includes two times and the new concepts of two-time work, kinetic energy, and of a two-time heat exchange that can be related to a nonequilibrium "effective temperature". Numerical simulations of a chain of anharmonic oscillators and of a model for a molecular motor driven by ATP hydrolysis illustrate these points.
Physical Review Letters, 2013
The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtaine... more The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical non-equilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a net drift induced by friction. If the thermal bath is replaced by a granular gas, the well known granular ratchet effect also intervenes, becoming dominant at high collision rates. For our chosen wheel shape the granular effect acts in the opposite direction with respect to the frictioninduced torque, resulting in the inversion of the ratchet direction as the collision rate increases. We have realized a new granular ratchet experiment where both these ratchet effects are observed, as well as the predicted inversion at their crossover. Our discovery paves the way to the realization of micro and sub-micrometer Brownian motors in an equilibrium fluid, based purely upon nano-friction.
Physical Review E, 2008
A unified derivation of the off equilibrium fluctuation dissipation relations (FDR) is given for ... more A unified derivation of the off equilibrium fluctuation dissipation relations (FDR) is given for Ising and continous spins to arbitrary order, within the framework of Markovian stochastic dynamics. Knowledge of the FDR allows to develop zero field algorithms for the efficient numerical computation of the response functions. Two applications are presented. In the first one, the problem of probing for the existence of a growing cooperative length scale is considered in those cases, like in glassy systems, where the linear FDR is of no use. The effectiveness of an appropriate second order FDR is illustrated in the test case of the Edwards-Anderson spin glass in one and two dimensions. In the second one, the important problem of the definition of an off equilibrium effective temperature through the nonlinear FDR is considered. It is shown that, in the case of coarsening systems, the effective temperature derived from the second order FDR is consistent with the one obtained from the linear FDR. †lippiello@sa.infn.it ‡corberi@sa.infn.it ¶sarracino@sa.infn.it §zannetti@sa.infn.it PACS: 05.70.Ln, 75.40.Gb,
Physical Review E, 2013
The effect of Coulomb friction is studied in the framework of collisional ratchets. It turns out ... more The effect of Coulomb friction is studied in the framework of collisional ratchets. It turns out that the average drift of these devices can be expressed as the combination of a term related to the lack of equipartition between the probe and the surrounding bath, and a term featuring the average frictional force. We illustrate this general result in the asymmetric Rayleigh piston, showing how Coulomb friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath. An explicit analytical expression for the average velocity of the piston is obtained in the rare collision limit. Numerical simulations support the analytical findings.
Physical Review E, 2013
We report the study of an experimental granular Brownian motor, inspired by the one published in ... more We report the study of an experimental granular Brownian motor, inspired by the one published in Eshuis et al. [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating blade, the surfaces of which break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main difference of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance v(0)(2). We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions, with an average angular velocity <ω>~v(0)(3), and (ii) frequent collisions (FC), with <ω>~v(0). We also study the fluctuations of the angle spanned in a large-time interval Δθ, which in the FC regime is proportional to the work done upon the motor. We observe that the fluctuation relation is satisfied with a slope which weakly depends on the relative collision frequency.
Physical Review E, 2010
We discuss the relation between the fluctuation-dissipation relation derived by Chatelain and Ric... more We discuss the relation between the fluctuation-dissipation relation derived by Chatelain and Ricci-Tersenghi [C.Chatelain, J.Phys. A 36, 10739 (2003); F. Ricci-Tersenghi, Phys.Rev.E 68, 065104(R) (2003)] and that by Lippiello-Corberi-Zannetti [E. Lippiello, F. Corberi and M. Zannetti Phys. Rev. E 71, 036104 (2005)]. In order to do that, we re-derive the fluctuation-dissipation relation for systems of discrete variables evolving in discrete time via a stochastic non-equilibrium Markov process. The calculation is carried out in a general formalism comprising the Chatelain, Ricci-Tersenghi result and that by Lippiello-Corberi-Zannetti as special cases. The applicability, generality, and experimental feasibility of the two approaches is thoroughly discussed. Extending the analytical calculation to the variance of the response function we show the vantage of field-free numerical methods with respect to the standard method where the perturbation is applied. We also show that the signal to noise ratio is better (by a factor √ 2) in the algorithm of Lippiello-Corberi-Zannetti with respect to that of Chatelain-Ricci Tersenghi. PACS: 05.70.Ln, 75.40.Gb, 05.40.-a I. INTRODUCTION
Physical Review B, 2008
We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a ... more We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a generic observable to the appropriate correlation functions, for Markov systems. The relation, which takes a similar form for systems governed by a master equation or by a Langevin equation, can be derived to every order, in large generality with respect to the considered model, in equilibrium and out of equilibrium as well. On the basis of the fluctuation dissipation relation we propose a particular response function, namely the second order susceptibility of the two-particle correlation function, as an effective quantity to detect and quantify cooperative effects in glasses and disordered systems. We test this idea by numerical simulations of the Edwards-Anderson model in one and two dimensions.