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Andrea Cavagna

Publications and source records attributed to Andrea Cavagna.

84 records · Page 5Linked to original sources
arXiv2000

Coarsening Dynamics of a Nonconserved Field Advected by a Uniform Shear Flow

We consider the ordering kinetics of a nonconserved scalar field advected by a uniform shear flow. Using the Ohta-Jasnow-Kawasaki approximation, modified to allow for shear-induced anisotropy, we calculate the asymptotic time dependence of the characteristic length scales, L_parallel and L_perp, that describe the growth of order parallel and perpendicular to the mean domain orientation. In space dimension d=3 we find, up to constants, L_parallel = gamma t^{3/2}, L_perp = t^{1/2}, where gamma is the shear rate, while for d = 2 we find L_parallel = gamma^{1/2} t (ln t)^{1/4}, L_perp = gamma^{-1/2}(ln t)^{-1/4} . Our predictions for d=2 can be tested by experiments on twisted nematic liquid crystals.

cond-mat.stat-mech↗
arXiv1999

A new approach for the analytic computation of the Instantaneous Normal Modes spectrum

In the context of the Instantaneous Normal Mode approach, the spectrum of the Hessian of Hamiltonian is a key quantity to describe liquids behaviour. The determination of the spectrum represents a major task for theoretical studies, and has been addressed recently in various works. In this paper a new approach for the analytic computation of the Hessian spectrum is presented. The one dimensional case for a system of particles interacting via a purely repulsive potential at low density is analyzed in details and the spectrum is computed exactly also in the localized sector. Finally, the possible extensions of the method are discussed, together with a comparison with different approaches to the problem.

cond-mat.stat-mech↗
arXiv1999

Index Distribution of Random Matrices with an Application to Disordered Systems

We compute the distribution of the number of negative eigenvalues (the index) for an ensemble of Gaussian random matrices, by means of the replica method. This calculation has important applications in the context of statistical mechanics of disordered systems, where the second derivative of the potential energy (the Hessian) is a random matrix whose negative eigenvalues measure the degree of instability of the energy surface. An analysis of the probability distribution of the Hessian index is therefore relevant for a geometric characterization of the energy landscape in disordered systems. The approach we use here is particularly suitable for this purpose, since it addresses the problem without any a priori assumption on the random matrix ensemble and can be naturally extended to more realistic, non-Gaussian distributions.

cond-mat.stat-mech↗
arXiv1999

A thermal model for adaptive competition in a market

New continuous and stochastic extensions of the minority game, devised as a fundamental model for a market of competitive agents, are introduced and studied in the context of statistical physics. The new formulation reproduces the key features of the original model, without the need for some of its special assumptions and, most importantly, it demonstrates the crucial role of stochastic decision-making. Furthermore, this formulation provides the exact but novel non-linear equations for the dynamics of the system.

cond-mat.stat-mech↗
arXiv1999

Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids

We analytically compute the spectrum of the Hessian of the Hamiltonian for a system of N particles interacting via a purely repulsive potential in one dimension. Our approach is valid in the low density regime, where we compute the exact spectrum also in the localized sector. We finally perform a numerical analysis of the localization properties of the eigenfunctions.

cond-mat.stat-mech↗
arXiv1998

Energy distribution of maxima and minima in a one-dimensional random system

We study the energy distribution of maxima and minima of a simple one-dimensional disordered Hamiltonian. We find that in systems with short range correlated disorder there is energy separation between maxima and minima, such that at fixed energy only one kind of stationary points is dominant in number over the other. On the other hand, in the case of systems with long range correlated disorder maxima and minima are completely mixed.

cond-mat.dis-nn↗
arXiv1998

Irrelevance of memory in the minority game

By means of extensive numerical simulations we show that all the distinctive features of the minority game introduced by Challet and Zhang (1997), are completely independent from the memory of the agents. The only crucial requirement is that all the individuals must posses the same information, irrespective of the fact that this information is true or false.

cond-mat.stat-mech↗
arXiv1998

Quenched complexity of the p-spin spherical spin-glass with external magnetic field

We consider the p-spin spherical spin-glass model in the presence of an external magnetic field as a general example of a mean-field system where a one step replica symmetry breaking (1-RSB) occurs. In this context we compute the complexity of the Thouless-Anderson-Palmer states, performing a quenched computation. We find what is the general connection between this method and the standard static 1-RSB one, formulating a clear mapping between the parameters used in the two different calculations. We also perform a dynamical analysis of the model, by which we confirm the validity of our results.

cond-mat.dis-nn↗
arXiv1997

On the stationary points of the TAP free energy

In the context of the p-spin spherical model, we introduce a method for the computation of the number of stationary points of any nature (minima, saddles, etc.) of the TAP free energy. In doing this we clarify the ambiguities related to the approximations usually adopted in the standard calculations of the number of states in mean field spin glass models.

cond-mat.dis-nn↗
arXiv1997

An investigation of the hidden structure of states in a mean field spin glass model

We study the geometrical structure of the states in the low temperature phase of a mean field model for generalized spin glasses, the p-spin spherical model. This structure cannot be revealed by the standard methods, mainly due to the presence of an exponentially high number of states, each one having a vanishing weight in the thermodynamic limit. Performing a purely entropic computation, based on the TAP equations for this model, we define a constrained complexity which gives the overlap distribution of the states. We find that this distribution is continuous, non-random and highly dependent on the energy range of the considered states. Furthermore, we show which is the geometrical shape of the threshold landscape, giving some insight into the role played by threshold states in the dynamical behaviour of the system.

cond-mat.dis-nn↗
arXiv1996

Structure of metastable states in spin glasses by means of a three replica potential

We introduce a three replica potential useful to examine the structure of metastables states above the static transition temperature, in the spherical p-spin model. Studying the minima of the potential we are able to find which is the distance between the nearest equilibrium and local equilibrium states, obtaining in this way information on the dynamics of the system. Furthermore, the analysis of the potential at the dynamical transition temperature suggests that equilibrium states are not randomly distributed in the phase space.

cond-mat.dis-nn↗