Potential energy landscape-based extended van der Waals equation

The inherent structures ({\it IS}) are the local minima of the potential energy surface or landscape, $U({\bf r})$, of an {\it N} atom system. Stillinger has given an exact {\it IS} formulation of thermodynamics. Here the implications for the equation of state are investigated. It is shown that the van der Waals ({\it vdW}) equation, with density-dependent $a$ and $b$ coefficients, holds on the high-temperature plateau of the averaged {\it IS} energy. However, an additional ``landscape'' contribution to the pressure is found at lower $T$. The resulting extended {\it vdW} equation, unlike the original, is capable of yielding a water-like density anomaly, flat isotherms in the coexistence region {\it vs} {\it vdW} loops, and several other desirable features. The plateau energy, the width of the distribution of {\it IS}, and the ``top of the landscape'' temperature are simulated over a broad reduced density range, $2.0 \ge \rho \ge 0.20$, in the Lennard-Jones fluid. Fits to the data yield an explicit equation of state, which is argued to be useful at high density; it nevertheless reproduces the known values of $a$ and $b$ at the critical point

Inherent-Structure Dynamics and Diffusion in Liquids

The self-diffusion constant D is expressed in terms of transitions among the local minima of the potential (inherent structure, IS) and their correlations. The formulae are evaluated and tested against simulation in the supercooled, unit-density Lennard-Jones liquid. The approximation of uncorrelated IS-transition (IST) vectors, D_{0}, greatly exceeds D in the upper temperature range, but merges with simulation at reduced T ~ 0.50. Since uncorrelated IST are associated with a hopping mechanism, the condition D ~ D_{0} provides a new way to identify the crossover to hopping. The results suggest that theories of diffusion in deeply supercooled liquids may be based on weakly correlated IST.Comment: submitted to PR

The Potential Energy Landscape and Mechanisms of Diffusion in Liquids

The mechanism of diffusion in supercooled liquids is investigated from the potential energy landscape point of view, with emphasis on the crossover from high- to low-T dynamics. Molecular dynamics simulations with a time dependent mapping to the associated local mininum or inherent structure (IS) are performed on unit-density Lennard-Jones (LJ). New dynamical quantities introduced include r2_{is}(t), the mean-square displacement (MSD) within a basin of attraction of an IS, R2(t), the MSD of the IS itself, and g_{loc}(t) the mean waiting time in a cooperative region. At intermediate T, r2_{is}(t) posesses an interval of linear t-dependence allowing calculation of an intrabasin diffusion constant D_{is}. Near T_{c} diffusion is intrabasin dominated with D = D_{is}. Below T_{c} the local waiting time tau_{loc} exceeds the time, tau_{pl}, needed for the system to explore the basin, indicating the action of barriers. The distinction between motion among the IS below T_{c} and saddle, or border dynamics above T_{c} is discussed.Comment: submitted to pr

A test of non-equilibrium thermodynamics in glassy systems: the soft-sphere case

The scaling properties of the soft-sphere potential allow the derivation of an exact expression for the pressure of a frozen liquid, i.e., the pressure corresponding to configurations which are local minima in its multidimensional potential energy landscape. The existence of such a relation offers the unique possibility for testing the recently proposed extension of the liquid free energy to glassy out-of-equilibrium conditions and the associated expression for the temperature of the configurational degrees of freedom. We demonstrate that the non-equilibrium free energy provides an exact description of the soft-sphere pressure in glass states

Energy landscape, two-level systems and entropy barriers in Lennard-Jones clusters

We develop an efficient numerical algorithm for the identification of a large number of saddle points of the potential energy function of Lennard- Jones clusters. Knowledge of the saddle points allows us to find many thousand adjacent minima of clusters containing up to 80 argon atoms and to locate many pairs of minima with the right characteristics to form two-level systems (TLS). The true TLS are singled out by calculating the ground-state tunneling splitting. The entropic contribution to all barriers is evaluated and discussed.Comment: 4 pages, RevTex, 2 PostScript figure

A Generalization of the Stillinger-Lovett Sum Rules for the Two-Dimensional Jellium

In the equilibrium statistical mechanics of classical Coulomb fluids, the long-range tail of the Coulomb potential gives rise to the Stillinger-Lovett sum rules for the charge correlation functions. For the jellium model of mobile particles of charge $q$ immersed in a neutralizing background, the fixing of one of the $q$-charges induces a screening cloud of the charge density whose zeroth and second moments are determined just by the Stillinger-Lovett sum rules. In this paper, we generalize these sum rules to the screening cloud induced around a pointlike guest charge $Z q$ immersed in the bulk interior of the 2D jellium with the coupling constant $\Gamma=\beta q^2$ ($\beta$ is the inverse temperature), in the whole region of the thermodynamic stability of the guest charge $Z>-2/\Gamma$. The derivation is based on a mapping technique of the 2D jellium at the coupling $\Gamma$ = (even positive integer) onto a discrete 1D anticommuting-field theory; we assume that the final results remain valid for all real values of $\Gamma$ corresponding to the fluid regime. The generalized sum rules reproduce for arbitrary coupling $\Gamma$ the standard Z=1 and the trivial Z=0 results. They are also checked in the Debye-H\"uckel limit $\Gamma\to 0$ and at the free-fermion point $\Gamma=2$. The generalized second-moment sum rule provides some exact information about possible sign oscillations of the induced charge density in space.Comment: 16 page

Cluster Monte Carlo study of multi-component fluids of the Stillinger-Helfand and Widom-Rowlinson type

Phase transitions of fluid mixtures of the type introduced by Stillinger and Helfand are studied using a continuum version of the invaded cluster algorithm. Particles of the same species do not interact, but particles of different types interact with each other via a repulsive potential. Examples of interactions include the Gaussian molecule potential and a repulsive step potential. Accurate values of the critical density, fugacity and magnetic exponent are found in two and three dimensions for the two-species model. The effect of varying the number of species and of introducing quenched impurities is also investigated. In all the cases studied, mixtures of $q$-species are found to have properties similar to $q$-state Potts models.Comment: 25 pages, 5 figure

Water-like anomalies for core-softened models of fluids: One dimension

We use a one-dimensional (1d) core-softened potential to develop a physical picture for some of the anomalies present in liquid water. The core-softened potential mimics the effect of hydrogen bonding. The interest in the 1d system stems from the facts that closed-form results are possible and that the qualitative behavior in 1d is reproduced in the liquid phase for higher dimensions. We discuss the relation between the shape of the potential and the density anomaly, and we study the entropy anomaly resulting from the density anomaly. We find that certain forms of the two-step square well potential lead to the existence at T=0 of a low-density phase favored at low pressures and of a high-density phase favored at high pressures, and to the appearance of a point $C'$ at a positive pressure, which is the analog of the T=0 ``critical point'' in the $1d$ Ising model. The existence of point $C'$ leads to anomalous behavior of the isothermal compressibility $K_T$ and the isobaric specific heat $C_P$.Comment: 22 pages, 7 figure

Structure optimization in an off-lattice protein model

We study an off-lattice protein toy model with two species of monomers interacting through modified Lennard-Jones interactions. Low energy configurations are optimized using the pruned-enriched-Rosenbluth method (PERM), hitherto employed to native state searches only for off lattice models. For 2 dimensions we found states with lower energy than previously proposed putative ground states, for all chain lengths $\ge 13$. This indicates that PERM has the potential to produce native states also for more realistic protein models. For $d=3$, where no published ground states exist, we present some putative lowest energy states for future comparison with other methods.Comment: 4 pages, 2 figure

Thermodynamics and statistical mechanics of frozen systems in inherent states

We discuss a Statistical Mechanics approach in the manner of Edwards to the ``inherent states'' (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity the inherent states are distributed according a generalized Gibbs measure obtained assuming the validity of the principle of maximum entropy, under suitable constraints. In particular we consider three lattice models (a diluted Spin Glass, a monodisperse hard-sphere system under gravity and a hard-sphere binary mixture under gravity) undergoing a schematic ``tap dynamics'', showing via Monte Carlo calculations that the time average of macroscopic quantities over the tap dynamics and over such a generalized distribution coincide. We also discuss about the general validity of this approach to non thermal systems.Comment: 10 pages, 16 figure