Searcharxiv⌕ Search

arXiv subjects

Francesco Zamponi

Publications and source records attributed to Francesco Zamponi.

At least 145 records · Page 8Linked to original sources
arXiv2011

On the solution of a `solvable' model of an ideal glass of hard spheres displaying a jamming transition

We discuss the analytical solution through the cavity method of a mean field model that displays at the same time an ideal glass transition and a set of jamming points. We establish the equations describing this system, and we discuss some approximate analytical solutions and a numerical strategy to solve them exactly. We compare these methods and we get insight into the reliability of the theory for the description of finite dimensional hard spheres.

cond-mat.dis-nn↗
arXiv2010

Can the jamming transition be described using equilibrium statistical mechanics?

When materials such as foams or emulsions are compressed, they display solid behaviour above the so-called `jamming' transition. Because compression is done out-of-equilibrium in the absence of thermal fluctuations, jamming appears as a new kind of a nonequilibrium phase transition. In this proceeding paper, we suggest that tools from equilibrium statistical mechanics can in fact be used to describe many specific features of the jamming transition. Our strategy is to introduce thermal fluctuations and use statistical mechanics to describe the complex phase behaviour of systems of soft repulsive particles, before sending temperature to zero at the end of the calculation. We show that currently available implementations of standard tools such as integral equations, mode-coupling theory, or replica calculations all break down at low temperature and large density, but we suggest that new analytical schemes can be developed to provide a fully microscopic, quantitative description of the jamming transition.

cond-mat.stat-mech↗
arXiv2010

Application of Edwards' statistical mechanics to high dimensional jammed sphere packings

The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling $ϕ\sim d\,2^{-d}$ is consistent with that of other approaches, such as replica theory and density functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.

cond-mat.stat-mech↗
arXiv2010

A solvable model of quantum random optimization problems

We study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian, characterized by an abrupt condensation transition and a continuum of level crossings as a function of the transverse field. We expect this complex structure to have deep consequences on the behavior of quantum algorithms attempting to find solutions to these problems.

cond-mat.stat-mech↗
arXiv2010

Mean field theory of hard sphere glasses and jamming

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the FCC lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g, a crystal) in low enough dimension. Still, amorphous packings have attracted a lot of interest, because for polydisperse colloids and granular materials the crystalline state is not obtained in experiments for kinetic reasons. We review here a theory of amorphous packings, and more generally glassy states, of hard spheres that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. In dimensions between two and six these predictions can be successfully compared with numerical simulations. We will also discuss the limit of large dimension where an exact solution is possible. Some of the results we present here have been already published, but others are original: in particular we improved the discussion of the large dimension limit and we obtained new results on the correlation function and the contact force distribution in three dimensions. We also try here to clarify the main assumptions that are beyond our theory and in particular the relation between our static computation and the dynamical procedures used to construct amorphous packings.

cond-mat.dis-nn↗
arXiv2009

Bose-Einstein condensation in quantum glasses

The role of geometrical frustration in strongly interacting bosonic systems is studied with a combined numerical and analytical approach. We demonstrate the existence of a novel quantum phase featuring both Bose-Einstein condensation and spin-glass behaviour. The differences between such a phase and the otherwise insulating "Bose glasses" are elucidated.

cond-mat.dis-nn↗
arXiv2009

Exact solution of the Bose-Hubbard model on the Bethe lattice

The exact solution of a quantum Bethe lattice model in the thermodynamic limit amounts to solve a functional self-consistent equation. In this paper we obtain this equation for the Bose-Hubbard model on the Bethe lattice, under two equivalent forms. The first one, based on a coherent state path integral, leads in the large connectivity limit to the mean field treatment of Fisher et al. [Phys. Rev. B {\bf 40}, 546 (1989)] at the leading order, and to the bosonic Dynamical Mean Field Theory as a first correction, as recently derived by Byczuk and Vollhardt [Phys. Rev. B {\bf 77}, 235106 (2008)]. We obtain an alternative form of the equation using the occupation number representation, which can be easily solved with an arbitrary numerical precision, for any finite connectivity. We thus compute the transition line between the superfluid and Mott insulator phases of the model, along with thermodynamic observables and the space and imaginary time dependence of correlation functions. The finite connectivity of the Bethe lattice induces a richer physical content with respect to its infinitely connected counterpart: a notion of distance between sites of the lattice is preserved, and the bosons are still weakly mobile in the Mott insulator phase. The Bethe lattice construction can be viewed as an approximation to the finite dimensional version of the model. We show indeed a quantitatively reasonable agreement between our predictions and the results of Quantum Monte Carlo simulations in two and three dimensions.

cond-mat.quant-gas↗
arXiv2009

A theory of amorphous packings of binary mixtures of hard spheres

We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical protocols can be identified with the infinite pressure limit of long lived metastable glassy states. We test this assumption against numerical and experimental data and show that the theory correctly reproduces the variation with mixture composition of structural observables, such as the total packing fraction and the partial coordination numbers.

cond-mat.dis-nn↗
arXiv2009

Time-dependent Nonlinear Optical Susceptibility of an Out-of-Equilibrium Soft Material

We investigate the time-dependent nonlinear optical absorption of a clay dispersion (Laponite) in organic dye (Rhodamine B) water solution displaying liquid-arrested state transition. Specifically, we determine the characteristic time $τ_D$ of the nonlinear susceptibility build-up due as to the Soret effect. By comparing $τ_D$ with the relaxation time provided by standard dynamic light scattering measurements we report on the decoupling of the two collective diffusion times at the two very different length scales during the aging of the out-of-equilibrium system. With this demonstration experiment we also show the potentiality of nonlinear optics measurements in the study of the late stage of arrest in soft materials.

cond-mat.soft↗
arXiv2008

Dynamical modelling of molecular constructions and setups for DNA unzipping

We present a dynamical model of DNA mechanical unzipping under the action of a force. The model includes the motion of the fork in the sequence-dependent landscape, the trap(s) acting on the bead(s), and the polymeric components of the molecular construction (unzipped single strands of DNA, and linkers). Different setups are considered to test the model, and the outcome of the simulations is compared to simpler dynamical models existing in the literature where polymers are assumed to be at equilibrium.

q-bio.BM↗
arXiv2008

Theory of the superglass phase

A superglass is a phase of matter which is characterized at the same time by superfluidity and a frozen amorphous structure. We introduce a model of interacting bosons in three dimensions that displays this phase unambiguously and that can be analyzed exactly or using controlled approximations. Employing a mapping between quantum Hamiltonians and classical Fokker-Planck operators, we show that the ground state wavefunction of the quantum model is proportional to the Boltzmann measure of classical hard spheres. This connection allows us to obtain quantitative results on static and dynamic quantum correlation functions. In particular, by translating known results on the glassy dynamics of Brownian hard spheres we work out the properties of the superglass phase and of the quantum phase transition between the superfluid and the superglass phase.

cond-mat.dis-nn↗
arXiv2008

On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations

The cavity method is a well established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann et al. [arXiv:0706.4391] proposed recently an extension of this method to quantum spin-1/2 models in a transverse field, using a discretized Suzuki-Trotter imaginary time formalism. Here we show how to take analytically the continuous imaginary time limit. Our main technical contribution is an explicit procedure to generate the spin trajectories in a path integral representation of the imaginary time dynamics. As a side result we also show how this procedure can be used in simple heat-bath like Monte Carlo simulations of generic quantum spin models. The replica symmetric continuous time quantum cavity method is formulated for a wide class of models, and applied as a simple example on the Bethe lattice ferromagnet in a transverse field. The results of the methods are confronted with various approximation schemes in this particular case. On this system we performed quantum Monte Carlo simulations that confirm the exactness of the cavity method in the thermodynamic limit.

cond-mat.stat-mech↗
arXiv2008

A review of the Statistical Mechanics approach to Random Optimization Problems

We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these problems, starting from basic concepts. We also discuss how statistical mechanics methods can be used to investigate the behavior of local search and decimation based algorithms.

cs.CC↗
arXiv2007

Relationship between clustering and algorithmic phase transitions in the random k-XORSAT model and its NP-complete extensions

We study the performances of stochastic heuristic search algorithms on Uniquely Extendible Constraint Satisfaction Problems with random inputs. We show that, for any heuristic preserving the Poissonian nature of the underlying instance, the (heuristic-dependent) largest ratio $α_a$ of constraints per variables for which a search algorithm is likely to find solutions is smaller than the critical ratio $α_d$ above which solutions are clustered and highly correlated. In addition we show that the clustering ratio can be reached when the number k of variables per constraints goes to infinity by the so-called Generalized Unit Clause heuristic.

cs.CC↗
arXiv2007

Dynamically correlated regions and configurational entropy in supercooled liquids

When a liquid is cooled below its melting temperature, if crystallization is avoided, it forms a glass. This phenomenon, called glass transition, is characterized by a marked increase of viscosity, about 14 orders of magnitude, in a narrow temperature interval. The microscopic mechanism behind the glass transition is still poorly understood. However, recently, great advances have been made in the identification of cooperative rearranging regions, or dynamical heterogeneities, i.e. domains of the liquid whose relaxation is highly correlated. The growth of the size of these domains is now believed to be the driving mechanism for the increase of the viscosity. Recently a tool to quantify the size of these domains has been proposed. We apply this tool to a wide class of materials to investigate the correlation between the size of the heterogeneities and their configurational entropy, i.e. the number of states accessible to a correlated domain. We find that the relaxation time of a given system, apart from a material dependent pre-factor, is a universal function of the configurational entropy of a correlated domain. As a consequence, we find that at the glass transition temperature, the size of the domains and the configurational entropy per unit volume are anti-correlated, as originally predicted by the Adam-Gibbs theory. Finally, we use our data to extract some exponents defined in the framework of the Random First Order Theory, a recent quantitative theory of the glass transition.

cond-mat.dis-nn↗
arXiv2006

Can rare SAT formulas be easily recognized? On the efficiency of message passing algorithms for K-SAT at large clause-to-variable ratios

For large clause-to-variable ratio, typical K-SAT instances drawn from the uniform distribution have no solution. We argue, based on statistical mechanics calculations using the replica and cavity methods, that rare satisfiable instances from the uniform distribution are very similar to typical instances drawn from the so-called planted distribution, where instances are chosen uniformly between the ones that admit a given solution. It then follows, from a recent article by Feige, Mossel and Vilenchik, that these rare instances can be easily recognized (in O(log N) time and with probability close to 1) by a simple message-passing algorithm.

cs.CC↗
arXiv2006

Glassy behavior of light in random lasers

A theoretical analysis [Angelani et al., Phys. Rev. Lett. 96, 065702 (2006)] predicts glassy behaviour of light in a nonlinear random medium. This implies slow dynamics related to the presence of many metastable states. We consider very general equations (that also apply to other systems, like Bose-Condensed gases) describing light in a disordered non-linear medium and through some approximations we relate them to a mean-field spin-glass-like model. The model is solved by the replica method, and replica-symmetry breaking phase transition is predicted. The transition describes a mode-locking process in which the phases of the modes are locked to random (history and sample-dependent) values. The results are based on very general theory, and embrace a variety of physical phenomena.

cond-mat.dis-nn↗