DOI

1

Field-induced superdiffusion and dynamical heterogeneity - Gradenigo, Giacomo and Bertin, Eric and Biroli, Giulio

PHYSICAL REVIEW E 93, (2016)

Abstract : By analyzing two kinetically constrained models of supercooled liquids we show that the anomalous transport of a driven tracer observed in supercooled liquids is another facet of the phenomenon of dynamical heterogeneity. We focus on the Fredrickson-Andersen and the Bertin-Bouchaud-Lequeux models. By numerical simulations and analytical arguments we demonstrate that the violation of the Stokes-Einstein relation and the field-induced superdiffusion observed during a long preasymptotic regime have the same physical origin: while a fraction of probes do not move, others jump repeatedly because they are close to local mobile regions. The anomalous fluctuations observed out of equilibrium in the presence of a pulling force epsilon, sigma(2)(x) (t) = < x(epsilon)(2) (t)> - < x(epsilon)(2)(t)>(2) similar to t(3/2), which are accompanied by the asymptotic decay alpha(epsilon) (t) similar to t(-1/2) of the non-Gaussian parameter from nontrivial values to zero, are due to the splitting of the probes population in the two (mobile and immobile) groups and to dynamical correlations, a mechanism expected to happen generically in supercooled liquids.

PHYSICAL REVIEW E 93, (2016)

LPS

Abstract : By analyzing two kinetically constrained models of supercooled liquids we show that the anomalous transport of a driven tracer observed in supercooled liquids is another facet of the phenomenon of dynamical heterogeneity. We focus on the Fredrickson-Andersen and the Bertin-Bouchaud-Lequeux models. By numerical simulations and analytical arguments we demonstrate that the violation of the Stokes-Einstein relation and the field-induced superdiffusion observed during a long preasymptotic regime have the same physical origin: while a fraction of probes do not move, others jump repeatedly because they are close to local mobile regions. The anomalous fluctuations observed out of equilibrium in the presence of a pulling force epsilon, sigma(2)(x) (t) = < x(epsilon)(2) (t)> - < x(epsilon)(2)(t)>(2) similar to t(3/2), which are accompanied by the asymptotic decay alpha(epsilon) (t) similar to t(-1/2) of the non-Gaussian parameter from nontrivial values to zero, are due to the splitting of the probes population in the two (mobile and immobile) groups and to dynamical correlations, a mechanism expected to happen generically in supercooled liquids.

DOI

2

From non-ergodic eigenvectors to local resolvent statistics and back: A random matrix perspective - Facoetti, Davide and Vivo, Pierpaolo and Biroli, Giulio

EPL 115, (2016)

Abstract : We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter N x N random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase. Interpreting the model as the combination of on-site random energies \a(i)\ and a structurally disordered hopping, we found that each eigenstate is delocalised over N2-gamma sites close in energy vertical bar a(j) - a(i)vertical bar = N1-gamma in agreement with Kravtsov et al. (New J. Phys., 17 (2015) 122002). Our other main result, obtained combining a recurrence relation for the resolvent matrix with insights from Dyson's Brownian motion, is to show that the properties of the non-ergodic delocalised phase can be probed studying the statistics of the local resolvent in a non-standard scaling limit. Copyright (C) EPLA, 2016

EPL 115, (2016)

LPS

Abstract : We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter N x N random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase. Interpreting the model as the combination of on-site random energies \a(i)\ and a structurally disordered hopping, we found that each eigenstate is delocalised over N2-gamma sites close in energy vertical bar a(j) - a(i)vertical bar = N1-gamma in agreement with Kravtsov et al. (New J. Phys., 17 (2015) 122002). Our other main result, obtained combining a recurrence relation for the resolvent matrix with insights from Dyson's Brownian motion, is to show that the properties of the non-ergodic delocalised phase can be probed studying the statistics of the local resolvent in a non-standard scaling limit. Copyright (C) EPLA, 2016

DOI

3

Breakdown of elasticity in amorphous solids - Biroli, Giulio and Urbani, Pierfrancesco

Nature Physics 12, 1130-1133 (2016)

Abstract : What characterizes a solid is the way that it responds to external stresses. Ordered solids, such as crystals, exhibit an elastic regime followed by a plastic regime, both understood microscopically in terms of lattice distortion and dislocations. For amorphous solids the situation is instead less clear, and the microscopic understanding of the response to deformation and stress is a very active research topic. Several studies have revealed that even in the elastic regime the response is very jerky at low temperature, resembling very much the response of disordered magnetic materials(1-6). Here we show that in a very large class of amorphous solids this behaviour emerges upon decreasing temperature, as a phase transition, where standard elastic behaviour breaks down. At the transition all nonlinear elastic moduli diverge and standard elasticity theory no longer holds. Below the transition, the response to deformation becomes history- and time-dependent.

Nature Physics 12, 1130-1133 (2016)

LPS

Abstract : What characterizes a solid is the way that it responds to external stresses. Ordered solids, such as crystals, exhibit an elastic regime followed by a plastic regime, both understood microscopically in terms of lattice distortion and dislocations. For amorphous solids the situation is instead less clear, and the microscopic understanding of the response to deformation and stress is a very active research topic. Several studies have revealed that even in the elastic regime the response is very jerky at low temperature, resembling very much the response of disordered magnetic materials(1-6). Here we show that in a very large class of amorphous solids this behaviour emerges upon decreasing temperature, as a phase transition, where standard elastic behaviour breaks down. At the transition all nonlinear elastic moduli diverge and standard elasticity theory no longer holds. Below the transition, the response to deformation becomes history- and time-dependent.

DOI

4

Super-diffusion around the rigidity transition: Levy and the Lilliputians - Lechenault, F. and Candelier, R. and Dauchot, O. and Bouchaud, J. -P. and Biroli, G.

SOFT MATTER 6, 3059-3064 (2010)

Abstract : By analyzing the displacement statistics of an assembly of horizontally vibrated bi-disperse frictional grains in the vicinity of the jamming transition experimentally studied before (F. Lechenault, O. Dauchot, G. Biroli and J.-P. Bouchard, Europhys. Lett., 2008, 83, 46003), we establish that their superdiffusive motion is a genuine Levy flight, but with a `jump' size that is very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.

SOFT MATTER 6, 3059-3064 (2010)

LPS

Abstract : By analyzing the displacement statistics of an assembly of horizontally vibrated bi-disperse frictional grains in the vicinity of the jamming transition experimentally studied before (F. Lechenault, O. Dauchot, G. Biroli and J.-P. Bouchard, Europhys. Lett., 2008, 83, 46003), we establish that their superdiffusive motion is a genuine Levy flight, but with a `jump' size that is very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.