arXiv subjects

Francesco Zamponi

Publications and source records attributed to Francesco Zamponi.

At least 127 records · Page 7Linked to original sources

arXiv2013

Jamming transition of randomly pinned systems

We consider a system of hard spheres close to jamming, where translation invariance is broken by pinning a randomly chosen set of particles. Using two different protocols, we generate two kinds of packings at the jamming point, isostatic and hyperstatic packings. In the case where the packings are isostatic, jamming transition is not affected by random pinning: the jamming density is only slightly reduced, a generalized isostaticity condition holds, the system is marginally rigid over the entire glass phase, and the typical structural signatures of jamming are unchanged. Besides, random pinning does not have effect on the vibrational modes of the amorphous system, at least on the time and length scale that we are able to probe. For packings that are hyperstatic at jamming, the microscopic properties of the system are strongly affected by the random pinning: the frozen degrees of freedom introduce an excess of constraints that drives the system far from the mechanical marginality conditions and stabilize the low frequency modes of the system, shifting them to higher frequencies. The distance from the isostatic point seems to be the only relevant parameter in the system in both cases. These two cases are in contrast with the behavior of the plane waves of a crystal: the whole spectrum in this case is shifted to higher frequencies as soon as some particles are pinned.

cond-mat.dis-nn↗

arXiv2013

The effect of quantum fluctuations on the coloring of random graphs

We present a study of the coloring problem (antiferromagnetic Potts model) of random regular graphs, submitted to quantum fluctuations induced by a transverse field, using the quantum cavity method and quantum Monte-Carlo simulations. We determine the order of the quantum phase transition encountered at low temperature as a function of the transverse field and discuss the structure of the quantum spin glass phase. In particular, we conclude that the quantum adiabatic algorithm would fail to solve efficiently typical instances of these problems because of avoided level crossings within the quantum spin glass phase, caused by a competition between energetic and entropic effects.

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arXiv2013

Systematic expansion in the order parameter for replica theory of the dynamical glass transition

It has been shown recently that predictions from Mode-Coupling Theory for the glass transition of hard-spheres become increasingly bad when dimensionality increases, whereas replica theory predicts a correct scaling. Nevertheless if one focuses on the regime around the dynamical transition in three dimensions, Mode-Coupling results are far more convincing than replica theory predictions. It seems thus necessary to reconcile the two theoretic approaches in order to obtain a theory that interpolates between low-dimensional, Mode-Coupling results, and "mean-field" results from replica theory. Even though quantitative results for the dynamical transition issued from replica theory are not accurate in low dimensions, two different approximation schemes --small cage expansion and replicated Hyper-Netted-Chain (RHNC)-- provide the correct qualitative picture for the transition, namely a discontinuous jump of a static order parameter from zero to a finite value. The purpose of this work is to develop a systematic expansion around the RHNC result in powers of the static order parameter, and to calculate the first correction in this expansion. Interestingly, this correction involves the static three-body correlations of the liquid. More importantly, we separately demonstrate that higher order terms in the expansion are quantitatively relevant at the transition, and that the usual mode-coupling kernel, involving two-body direct correlation functions of the liquid, cannot be recovered from static computations.

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arXiv2013

Static replica approach to critical correlations in glassy systems

We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises because of the presence of soft modes and we derive an effective replica field theory for these critical fluctuations. By using this at the Gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls the Mode-Coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions. Moreover we perform a one-loop computation in order to identify the region in which the mean field Gaussian approximation is valid. The result is a Ginzburg criterion for the glass transition. We define and compute in this way a proper Ginzburg number. Finally, we present numerical values of all these quantities obtained from the Hypernetted Chain approximation for the replicated liquid theory.

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arXiv2012

Theory of simple glasses

This manuscript has been prepared as a thesis to obtain the French "Habilitation à diriger des recherches (HDR)" which allows one to supervise PhD students. I review here my work on the glass and jamming transition. I tried to explain this subject in a concise and self-contained way, highlighting what I consider the main motivations for its study and trying to put my work in a broader perspective. Basically I tried to tell this story in the same way as I would tell it to a student who contacted me to start a PhD thesis on these topics.

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arXiv2012

The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs

In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular Max-Cut. The cost functions associated with these two clause-based optimization problems are similar as they are both defined on 3-regular hypergraphs. For 3-regular 3-XORSAT the clauses contain three variables and for 3-regular Max-Cut the clauses contain two variables. The quantum adiabatic algorithms we study for these two problems use interpolating Hamiltonians which are stoquastic and therefore amenable to sign-problem free quantum Monte Carlo and quantum cavity methods. Using these techniques we find that the quantum adiabatic algorithm fails to solve either of these problems efficiently, although for different reasons.

quant-ph↗

arXiv2012

The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective

Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function (ground state energy). Random optimization problems provide a natural testbed to compare its efficiency with that of classical algorithms. These problems correspond to mean field spin glasses that have been extensively studied in the classical case. This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction.

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arXiv2012

Exact theory of dense amorphous hard spheres in high dimension. I. The free energy

We consider the theory of the glass transition and jamming of hard spheres in the large space dimension limit. Previous investigations were based on the assumption that the probability distribution within a "cage" is Gaussian, which is not fully consistent with numerical results. Here we perform a replica calculation without making any assumption on the cage shape. We show that thermodynamic functions turn out to be exact within the Gaussian ansatz -- provided one allows for arbitrary replica symmetry breaking --- and indeed agree well with numerical results. The actual structure function (the so-called non-ergodic parameter) is not Gaussian, an apparent paradox which we discuss. In this paper we focus on the free energy, future papers will present the results for the structure functions and a detailed comparison with numerical results.

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arXiv2012

Universal microstructure and mechanical stability of jammed packings

Jammed packings' mechanical properties depend sensitively on their detailed local structure. Here we provide a complete characterization of the pair correlation close to contact and of the force distribution of jammed frictionless spheres. In particular we discover a set of new scaling relations that connect the behavior of particles bearing small forces and those bearing no force but that are almost in contact. By performing systematic investigations for spatial dimensions d=3-10, in a wide density range and using different preparation protocols, we show that these scalings are indeed universal. We therefore establish clear milestones for the emergence of a complete microscopic theory of jamming. This description is also crucial for high-precision force experiments in granular systems.

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arXiv2012

Dimensional Study of the Caging Order Parameter at the Glass Transition

The glass problem is notoriously hard and controversial. Even at the mean-field level, little is agreed about how a fluid turns sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves self-caging, which provides an order parameter for the transition. It is also broadly assumed that this cage should have a Gaussian shape in the mean-field limit. Here we show that this ansatz does not hold. By performing simulations as a function of spatial dimension, we find the cage to keep a non-trivial form. Quantitative mean-field descriptions of the glass transition, such as mode-coupling theory, density functional theory, and replica theory, all miss this crucial element. Although the mean-field random first-order transition scenario of the glass transition is here qualitatively supported and non-mean-field corrections are found to remain small on decreasing dimension, reconsideration of its implementation is needed for it to result in a coherent description of experimental observations.

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arXiv2012

On the relation between kinetically constrained models of glass dynamics and the random first-order transition theory

In this paper we revisit and extend the mapping between two apparently different classes of models. The first class contains the prototypical models described --at the mean-field level-- by the Random First Order Transition (RFOT) theory of the glass transition, called either "random XORSAT problem" (in the information theory community) or "diluted $p$-spin model" (in the spin glass community), undergoing a single-spin flip Glauber dynamics. The models in the second class are Kinetically Constrained Models (KCM): their Hamiltonian is that of independent spins in a constant magnetic field, hence their thermodynamics is completely trivial, but the dynamics is such that only groups of spin can flip together, thus implementing a kinetic constraint that induces a non-trivial dynamical behavior. A mapping between some representatives of these two classes has been known for long. Here we formally prove this mapping at the level of the master equation, and we apply it to the particular case of Bethe lattice models. This allows us to show that a RFOT model can be mapped exactly into a KCM. However, the natural order parameter for the RFOT model, namely the spin overlap, is mapped into a very complicated non-local function in the KCM. Therefore, if one were to study the KCM without knowing of the mapping onto the RFOT model, one would guess that its physics is quite different from the RFOT one. Our results instead suggest that these two apparently different descriptions of the glass transition are, at least in some case, closely related.

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arXiv2012

A tentative replica theory of glassy Helium 4

We develop a quantum replica method for interacting particle systems and use it to estimate the location of the glass transition line in Helium 4. Although we do not fully succeed in taking into account all quantum effects, we make a thorough semiclassical analysis. We confirm previous suggestions that quantum fluctuations promote the formation of the glass and give a quantitative estimate of this effect at high density. Finally, we discuss the difficulties that are met when one tries to extend the calculation to the region of low densities and low temperatures, where quantum effects are strong and the semiclassical expansion breaks down.

cond-mat.dis-nn↗

arXiv2012

Transition path sampling algorithm for discrete many-body systems

We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions, including systems that are out of equilibrium. We combine the proposed path-sampling algorithm with thermodynamic integration to calculate transition rates. We demonstrate our method on the well studied 2D Ising model with periodic boundary conditions, and show agreement with other results both for large and small system sizes. The method scales well with the system size, allowing one to simulate systems with many degrees of freedom, and providing complementary information with respect to other algorithms.

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arXiv2011

Microscopic theory of the jamming transition of harmonic spheres

We develop a microscopic theory to analyze the phase behaviour and compute correlation functions of dense assemblies of soft repulsive particles both at finite temperature, as in colloidal materials, and at vanishing temperature, a situation relevant for granular materials and emulsions. We use a mean-field statistical mechanical approach which combines elements of liquid state theory to replica calculations to obtain quantitative predictions for the location of phase boundaries, macroscopic thermodynamic properties and microstructure of the system. We focus in particular on the derivation of scaling properties emerging in the vicinity of the jamming transition occurring at large density and zero temperature. The new predictions we obtain for pair correlation functions near contact are tested using computer simulations. Our work also clarifies the conceptual nature of the jamming transition, and its relation to the phenomenon of the glass transition observed in atomic liquids.

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arXiv2011

Glass transition and random close packing above three dimensions

Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static replica theory, but disagree with the dynamic mode-coupling theory, indicating that key ingredients of high-dimensional physics are missing from the latter. We also obtain numerical estimates of the random close packing density, which provides new insights into the mathematical problem of packing spheres in large dimension.

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arXiv2011

A microscopic mean-field theory of the jamming transition

Dense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions using fully equilibrium statistical mechanics and develop a microscopic many-body mean-field theory of the jamming transition for soft repulsive spherical particles. We derive analytically some of the scaling laws and exponents characterizing the transition and obtain predictions for microscopic correlation functions of jammed states that are amenable to experimental verifications, and whose accuracy we confirm using computer simulations.

cond-mat.stat-mech↗

arXiv2011

Leggett's bound for amorphous solids

We investigate the constraints on the superfluid fraction of an amorphous solid following from an upper bound derived by Leggett. In order to accomplish this, we use as input density profiles generated for amorphous solids in a variety of different manners including by investigating Gaussian fluctuations around classical results. These rough estimates suggest that, at least at the level of the upper bound, there is not much difference in terms of superfluidity between a glass and a crystal characterized by the same Lindemann ratio. Moreover, we perform Path Integral Monte Carlo simulations of distinguishable Helium 4 rapidly quenched from the liquid phase to very lower temperature, at the density of the freezing transition. We find that the system crystallizes very quickly, without any sign of intermediate glassiness. Overall our results suggest that the experimental observations of large superfluid fractions in Helium 4 after a rapid quench correspond to samples evolving far from equilibrium, instead of being in a stable glass phase. Other scenarios and comparisons to other results on the super-glass phase are also discussed.

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arXiv2011

The quantum Biroli-Mézard model: glass transition and superfluidity in a quantum lattice glass model

We study the quantum version of a lattice model whose classical counterpart captures the physics of structural glasses. We discuss the role of quantum fluctuations in such systems and in particular their interplay with the amorphous order developed in the glass phase. We show that quantum fluctuations might facilitate the formation of the glass at low enough temperature. We also show that the glass transition becomes a first-order transition between a superfluid and an insulating glass at very low temperature, and is therefore accompanied by phase coexistence between superfluid and glassy regions.

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