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arXiv2013

Glass and jamming transition of simple liquids: static and dynamic theory

We study the glass and jamming transition of finite-dimensional models of simple liquids: hard- spheres, harmonic spheres and more generally bounded pair potentials that modelize frictionless spheres in interaction. At finite temperature, we study their glassy dynamics via field-theoretic methods by resorting to a mapping towards an effective quantum mechanical evolution, and show that such an approach resolves several technical problems encountered with previous attempts. We then study the static, mean-field version of their glass transition via replica theory, and set up an expansion in terms of the corresponding static order parameter. Thanks to this expansion, we are able to make a direct and exact comparison between historical Mode-Coupling results and replica theory. Finally we study these models at zero temperature within the hypotheses of the random-first-order-transition theory, and are able to derive a quantitative mean-field theory of the jamming transition. The theoretic methods of field theory and liquid theory used in this work are presented in a mostly self-contained, and hopefully pedagogical, way. This manuscript is a corrected version of my PhD thesis, defended in June, 29th, under the advisorship of Frédéric van Wijland, and also contains the result of collaborations with Ludovic Berthier and Francesco Zamponi. The PhD work was funded by a CFM-JP Aguilar grant, and conducted in the Laboratory MSC at Université Denis Diderot--Paris 7, France.

cond-mat.dis-nn↗

arXiv2013

A simple phenomenologic model for particle transport in space-periodic potentials in underdamped systems

We consider the motion of an underdamped Brownian particle in a tilted periodic potential in a wide temperature range. Based on the previous data [1] and the new simulation results we show that the underdamped motion of particles in space-periodic potentials can be considered as the overdamped motion in the velocity space in the effective double-well potential. Simple analytic expressions for the particle mobility and diffusion coefficient have been derived with the use of the presented model. The results of analytical computations match well with numerical simulation data.

cond-mat.stat-mech↗

arXiv2013

Towards a Theory of the Glass Crossover

The standard field-theoretical procedure to study the effect of long wavelength fluctuations on a genuine second-order phase transition is applied to the Mode-Coupling-Theory (MCT) dynamical singularity at $T_c$ in the $β$ regime. Technically this is achieved by a dynamical field-theoretical decoration of MCT that can be studied by a loop expansion. An explicit computation shows that at all orders the leading contributions are the same of a dynamical stochastic glassy equation, {\it i.e} an extension of the standard MCT equation for the critical correlator with local random fluctuations of the separation parameter. It is suggested that the equation is an essential ingredient in the process that turns the singularity at $T_c$ into a dynamical crossover to activated dynamics.

cond-mat.dis-nn↗

arXiv2013

The structure of infectious disease outbreaks across the animal-human interface

Despite the enormous relevance of zoonotic infections to world- wide public health, and despite much effort in modeling individual zoonoses, a fundamental understanding of the disease dynamics and the nature of outbreaks arising in such systems is still lacking. We introduce a simple stochastic model of susceptible-infected- recovered dynamics in a coupled animal-human metapopulation, and solve analytically for several important properties of the cou- pled outbreaks. At early timescales, we solve for the probability and time of spillover, and the disease prevalence in the animal population at spillover as a function of model parameters. At long times, we characterize the distribution of outbreak sizes and the critical threshold for a large human outbreak, both of which show a strong dependence on the basic reproduction number in the animal population. The coupling of animal and human infection dynamics has several crucial implications, most importantly al- lowing for the possibility of large human outbreaks even when human-to-human transmission is subcritical.

q-bio.PE↗

arXiv2013

Anomalous fluctuation relations

We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for stochastic dynamics modeled by the ordinary Langevin equation. We then introduce three generic types of dynamics generating anomalous diffusion: Lévy flights, long-time correlated Gaussian stochastic processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the work probability distributions in the simple nonequilibrium situation of a particle subject to a constant force. This allows us to check the transient FR for anomalous dynamics. We find a new form of FRs, which is intimately related to the validity of fluctuation-dissipation relations. Analogous results are obtained for a particle in a harmonic potential dragged by a constant force. We argue that these findings are important for understanding fluctuations in experimentally accessible systems. As an example, we discuss the anomalous dynamics of biological cell migration both in equilibrium and in nonequilibrium under chemical gradients.

cond-mat.stat-mech↗

arXiv2013

Thermal conductivity of the chain with an asymmetric pair interaction

We provide molecular dynamics simulation of heat transport in one-dimensional molecular chains with different interparticle pair potentials. We show that the thermal conductivity is finite in the thermodynamic limit in the chains with the potential, which allows for bond dissociation. The Lennard-Jones, Morse and Coulomb potentials belong to such type of potentials. The convergence of the thermal conductivity is provided by phonon scattering on the locally stretched loose interatomic bonds at low temperature and by the many-particle scattering at high temperature. On the other hand, the chains with the confining pair potential, which does not allow for the bond dissociation, posses anomalous (diverging with the chain length) thermal conductivity. We emphasize that the chains with the symmetric or asymmetric Fermi-Pasta-Ulam potential or with the combined potentials containing parabolic confining potential all exhibit anomalous heat transport.

cond-mat.stat-mech↗

arXiv2013

Local pressure of confined fluids inside nanoslit pores -- A density functional theory prediction

In this work, the local pressure of fluids confined inside nanoslit pores is predicted within the framework of the density functional theory. The Euler-Lagrange equation in the density functional theory of statistical mechanics is used to obtain the force balance equation which leads to a general equation to predict the local normal component of the pressure tensor. Our approach yields a general equation for predicting the normal pressure of confined fluids and it satisfies the exact bulk thermodynamics equation when the pore width approaches infinity. As two basic examples, we report the solution of the general equation for hard-sphere (HS) and Lennard-Jones (LJ) fluids confined between two parallel-structureless hard walls. To do so, we use the modified fundamental measure theory (mFMT) to obtain the normal pressure for hard-sphere confined fluid and mFMT incorporated with the Rosenfeld perturbative DFT for the LJ fluid. Effects of different variables including pore width, bulk density and temperature on the behavior of normal pressure are studied and reported. Our predicted results show that in both HS and LJ cases the confined fluids normal pressure has an oscillatory behavior and the number of oscillations increases with bulk density and temperature. The oscillations also become broad and smooth with pore width at a constant temperature and bulk density. In comparison with the HS confined fluid, the values of normal pressure for the LJ confined fluid as well as its oscillations at all distances from the walls are less profound.

cond-mat.stat-mech↗

arXiv2013

Statistical Physics: a Short Course for Electrical Engineering Students

This is a set of lecture notes of a course on statistical physics and thermodynamics, which is oriented, to a certain extent, towards electrical engineering students. The main body of the lectures is devoted to statistical physics, whereas much less emphasis is given to the thermodynamics part. In particular, the idea is to let the most important results of thermodynamics (most notably, the laws of thermodynamics) to be obtained as conclusions from the derivations in statistical physics. Beyond the variety of central topics in statistical physics that are important to the general scientific education of the EE student, special emphasis is devoted to subjects that are vital to the engineering education concretely. These include, first of all, quantum statistics, like the Fermi-Dirac distribution, as well as diffusion processes, which are both fundamental for deep understanding of semiconductor devices. Another important issue for the EE student is to understand mechanisms of noise generation and stochastic dynamics in physical systems, most notably, in electric circuitry. Accordingly, the fluctuation-dissipation theorem of statistical mechanics, which is the theoretical basis for understanding thermal noise processes in systems, is presented from a signals--and--systems point of view, in a way that would hopefully be understandable and useful for an engineering student, and well connected to other courses in the electrcial engineering curriculum like courses on random priocesses. The quantum regime, in this context, is important too and hence provided as well. Finally, we touch very briefly upon some relationships between statistical mechanics and information theory, which is the theoretical basis for communications engineering, and demonstrate how statistical-mechanical approach can be useful in order for the study of information-theoretic problems.

cond-mat.stat-mech↗

arXiv2013

Wulff shape of equilibrium crystals

The shape of an equilibrium crystal is obtained, according to the Gibbs thermodynamic principle, by minimizing the total surface free energy associated to the crystal-medium interface. To study the solution to this problem, known as the Wulff construction, is the object of the article.

cond-mat.stat-mech↗

arXiv2013

Critical exponents in Ising Spin Glasses

Extensive simulations are made of the spin glass susceptibility and correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian and bimodal interaction distributions. Once the transition temperature is accurately established using a standard criterion, critical exponents and correction terms can be readily estimated by extrapolating measurements made in the thermodynamic limit regime. The data show that the critical exponents of the susceptibility $γ$ and of the correlation length $ν$ depend on the form of the interaction distribution. This observation implies that quite generally critical exponents are not universal in ISGs.

cond-mat.dis-nn↗

arXiv2013

Exact closed equation for reduced equilibrium distribution functions of the many-particle system

An exact closed equation for s - particle equilibrium distribution function (s >1 interacting particles is obtained. This integra-differential β - convolution equation (β=1/k_{B}T) follows from the Bloch equation for the canonical distribution function by applying the projection operator integrating off the coordinates of N-s irrelevant particles. The method of expansion of the obtained equation kernel in the particle density n is suggested. The solution to this equation in the linear in n approximation for the kernel is found.

cond-mat.stat-mech↗

arXiv2013

Variational Principle in Langevin Processes

The recent work, Nemoto and Sasa [Phys. Rev. E, 83: 030105(R) (2011)], has shown that large deviations of the current characterizing a nonequilibrium system are obtained by observing the typical current for a modified system specified by a variational principle. In the present study, we will give a generalized version of the Nemoto-Sasa study by extracting a hidden mathematical structure from the fluctuation-response relation which is well-known in statistical mechanics. Here, the minimization of the Kullback-Leibler divergence plays an essential role.

cond-mat.stat-mech↗

arXiv2013

Intrinsic structure of liquid surface and capillary waves on the Density Functional Theory

Two different theories are used to understand the liquid-vapor interfaces: the Van der Waals theory and the capillary waves theory. But comparing both come up a problem of interpretation of the interface density profiles obtained, for example, with the Density Functional Theory (DFT). As a consequence emerge the question of how the surface fluctuations are included on traditional density profiles (usually named equilibrium density profiles). Last years, new insights on the role of capillary waves were possible by analyzing X-ray reflectivity experiments and performing computer simulations of liquids with low melting temperature. In particular, the density profile exhibits a layering structure which is considered a key property to elucidate a new interpretation of those profiles as intrinsic density profiles. This dissertation aims to investigate these questions within the DFT using simple fluids with a pairwise interactions that reproduce important phase-diagram properties of liquid metals. Two generics questions were explored: the relevance of Fisher-Widom line and the role of capillary waves on the nature of interface obtained with approximations WDA and FMT. It hypothesized the existence of a density profile with strong layering properties whose structure is reduced by capillary waves. Then the effect of surface fluctuations is described by introducing an effective transversal size which imposes a limitation of the spectrum of surface fluctuations incorporated on the DFT. However, an explicit methodology to unfreeze the capillary waves over a postulated intrinsic profile exempt of surface fluctuations was proven still a challenge. As a consequence it suggested that other previous results describing the liquid surface using the equilibrium DFT may conduct to unphysical properties.

cond-mat.stat-mech↗

arXiv2013

Connecting active and passive microrheology in living cells

We use a model based on the fractional Langevin equation with external noise to describe the anomalous dynamics observed in microrheology experiments in living cells. This model reproduces both the subdiffusive short-time and the superdiffusive long-time behavior. We show that the former reflects the equilibrium properties of the cell, while the latter is due to the nonequilibrium external noise. This allows to infer the transport properties of the system under active measurements from the transient behavior obtained from passive measurements, extending the connection between active and passive microrheology to the nonequilibrium regime. The active and passive results can be linked via a generalized Stokes-Einstein relation based on an effective time-dependent temperature, which can be determined from the transient passive behavior. In order to reproduce experimental data, we further find that the external noise describing the active components of the cell has to be nonstationary. We establish that the latter leads to a time-dependent noise spectral density.

cond-mat.soft↗

arXiv2013

Universal scaling function for the two-dimensional Ising model in an external field: A pragmatic approach

We report an effective functional form for the spin-spin correlation function of the 2D Ising model as a function of temperature and field. Although the Ising model has been well studied, no analytical result for the spin-spin correlation function exists for arbitrary magnetic fields and temperatures. We show the validity of our form by comparison with simulations using the Wolff algorithm, and obtain remarkable precision by including analytic corrections to scaling. Given recent interest in comparing biomembrane heterogeneity to Ising criticality, our spin-spin correlation function may be used as a predictive quantitative measure for FRET or NMR membrane experiments.

cond-mat.stat-mech↗

arXiv2013

Violation of Fundamental Thermodynamic Law or Invalid Microstate Densities?

It is often incorrectly assumed that the number of microstates Ω(E,V,N,...) available to an isolated system can have arbitrary dependence on the extensive variables E,V,N, .... However, this is not the case for natural systems which can reach thermodynamic equilibrium since restrictions exist arising from the underlying equilibrium axioms of independence and \it{a priori} equal probability of microstate, and the fundamental constants of Nature. Here we derive a concise formula specifying the condition on Ω which must be met for real systems. Models which do not respect this condition will present inconsistencies when treated under equilibrium thermodynamic formalism. This has relevance to a number of recent models in which negative heat capacity and violation of fundamental thermodynamic law have been reported. Natural quantum systems obey the axioms and abide by the fundamental constants, and thus natural systems, in the absence of infinite range forces, can, in principle, attain thermodynamic equilibrium.

cond-mat.stat-mech↗

arXiv2013

A multi-phase, multi-component critical equation of state

Realistic equations of state valid in the whole state space of a multi-component mixture should satisfy at least three important constraints: (i) The Gibbs phase rule holds. (ii) At low densities, one can deduce a virial equation of state with the correct multi-component structure. (iii) Close to critical points, plait points, and consolute points, the correct universality and scaling behavior is guaranteed. This paper discusses semiempirical equations of state for mixtures that express the pressure as an explicit function of temperature and the chemical potentials. In the first part, expressions are derived for the most important thermodynamic quantities. The main result of the second part is the construction of a large family of equations of state with the properties (i)--(iii).

cond-mat.stat-mech↗

arXiv2013

The Dilemma of Bose Solids: is He Supersolid?

Nearly a decade ago the old controversy about possible superfluid flow in the ground state of solid He4 was revived by the apparent experimental observation of such superflow. Although the experimentalists have recently retracted, very publicly, some of the observations on which such a claim was based, other confirming observations of which there is no reason for doubt remain on the record. Meanwhile theoretical arguments bolstered by some experimental evidence strongly favor the existence of supersolidity in the Bose-Hubbard model, and these arguments would seem to extend to solid He. The true situation thus is apparently extraordinarily opaque. The situation is complicated by the fact that all accurate simulation studies on Heuse the uniform sign hypothesis which confines them to the phase-coherent state, which is, in principle, supersolid, so that no accurate simulations of the true, classical solid exist. There is great confusion as to the nature of the ground state wave-function for a bose quantum solid, and we suggest that until that question is cleared up none of these dilemmas will be resolved.

cond-mat.stat-mech↗