Diffusion and jump-length distribution in liquid and amorphous Cu33_{33}Zr67_{67}

Using molecular dynamics simulation, we calculate the distribution of atomic jum ps in Cu$_{33}$Zr$_{67}$ in the liquid and glassy states. In both states the distribution of jump lengths can be described by a temperature independent exponential of the length and an effective activation energy plus a contribution of elastic displacements at short distances. Upon cooling the contribution of shorter jumps dominates. No indication of an enhanced probability to jump over a nearest neighbor distance was found. We find a smooth transition from flow in the liquid to jumps in the g lass. The correlation factor of the diffusion constant decreases with decreasing temperature, causing a drop of diffusion below the Arrhenius value, despite an apparent Arrhenius law for the jump probability

Ac hopping conduction at extreme disorder takes place on the percolating cluster

Simulations of the random barrier model show that ac currents at extreme disorder are carried almost entirely by the percolating cluster slightly above threshold; thus contradicting traditional theories contributions from isolated low-activation-energy clusters are negligible. The effective medium approximation in conjunction with the Alexander-Orbach conjecture leads to an excellent analytical fit to the universal ac conductivity with no nontrivial fitting parameters

Isomorphs in model molecular liquids

Isomorphs are curves in the phase diagram along which a number of static and dynamic quantities are invariant in reduced units. A liquid has good isomorphs if and only if it is strongly correlating, i.e., the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of two systems of small rigid molecules, the asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for both systems we find that the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self part of the intermediate scattering function, the reduced molecular center-of-mass radial distribution function to a good approximation are invariant along an isomorph. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to another isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be more approximative than those of the asymmetric dumbbell model, which is consistent with the OTP model being less strongly correlating. For both models we find "master isomorphs", i.e., isomorphs have identical shape in the virial/potential energy phase diagram.Comment: 20 page

Communication: Studies of the Lennard-Jones fluid in 2, 3, and 4 dimensions highlight the need for a liquid-state 1/d expansion

The recent theoretical prediction by Maimbourg and Kurchan [arXiv:1603.05023] that for regular pair-potential systems the virial potential-energy correlation coefficient increases towards unity as the dimension $d$ goes to infinity is investigated for the standard 12-6 Lennard-Jones fluid. This is done by computer simulations for $d=2,3,4$ going from the critical point along the critical isotherm/isochore to higher density/temperature. In all cases the virial potential-energy correlation coefficient increases significantly. For a given density and temperature relative to the critical point, with increasing number of dimension the Lennard-Jones system conforms better to the hidden-scale-invariance property characterized by high virial potential-energy correlations (a property that leads to the existence of isomorphs in the thermodynamic phase diagram, implying that it becomes effectively one-dimensional in regard to structure and dynamics). The present paper also gives the first numerical demonstration of isomorph invariance of structure and dynamics in four dimensions. Our findings emphasize the need for a universally applicable $1/d$ expansion in liquid-state theory; we conjecture that the systems known to obey hidden scale invariance in three dimensions are those for which the yet-to-be-developed $1/d$ expansion converges rapidly

Observation of Single Transits in Supercooled Monatomic Liquids

A transit is the motion of a system from one many-particle potential energy valley to another. We report the observation of transits in molecular dynamics (MD) calculations of supercooled liquid argon and sodium. Each transit is a correlated simultaneous shift in the equilibrium positions of a small local group of particles, as revealed in the fluctuating graphs of the particle coordinates versus time. This is the first reported direct observation of transit motion in a monatomic liquid in thermal equilibrium. We found transits involving 2 to 11 particles, having mean shift in equilibrium position on the order of 0.4 R_1 in argon and 0.25 R_1 in sodium, where R_1 is the nearest neighbor distance. The time it takes for a transit to occur is approximately one mean vibrational period, confirming that transits are fast.Comment: 19 pages, 8 figure

Energy landscape of a Lennard-Jones liquid: Statistics of stationary points

Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well defined relation k(u) is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy, which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach the threshold energy at a temperature close to the mode-coupling transition temperature Tc.Comment: 4 RevTeX pages, 6 eps figures. Revised versio

Saddles in the energy landscape probed by supercooled liquids

We numerically investigate the supercooled dynamics of two simple model liquids exploiting the partition of the multi-dimension configuration space in basins of attraction of the stationary points (inherent saddles) of the potential energy surface. We find that the inherent saddles order and potential energy are well defined functions of the temperature T. Moreover, decreasing T, the saddle order vanishes at the same temperature (T_MCT) where the inverse diffusivity appears to diverge as a power law. This allows a topological interpretation of T_MCT: it marks the transition from a dynamics between basins of saddles (T>T_MCT) to a dynamics between basins of minima (T<T_MCT).Comment: 4 pages, 3 figures, to be published on PR

Growing Correlation Length on Cooling Below the Onset of Caging in a Simulated Glass-Forming Liquid

We present a calculation of a fourth-order, time-dependent density correlation function that measures higher-order spatiotemporall correlations of the density of a liquid. From molecular dynamics simulations of a glass-forming Lennard-Jones liquid, we find that the characteristic length scale of this function has a maximum as a function of time which increases steadily beyond the characteristic length of the static pair correlation function $g(r)$ in the temperature range approaching the mode coupling temperature from above

Invariants in the Yukawa system’s thermodynamic phase diagram

This paper shows that several known properties of the Yukawa system can be derived from the isomorph theory, which applies to any system that has strong correlations between its virial and potential-energy equilibrium fluctuations. Such "Roskilde-simple" systems have a simplified thermodynamic phase diagram deriving from the fact that they have curves (isomorphs) along which structure and dynamics in reduced units are invariant to a good approximation. We show that the Yukawa system has strong virial potential-energy correlations and identify its isomorphs by two different methods. One method, the so-called direct isomorph check, identifies isomorphs numerically from jumps of relatively small density changes (here 10%). The second method identifies isomorphs analytically from the pair potential. The curves obtained by the two methods are close to each other; these curves are confirmed to be isomorphs by demonstrating the invariance of the radial distribution function, the static structure factor, the mean-square displacement as a function of time, and the incoherent intermediate scattering function. Since the melting line is predicted to be an isomorph, the theory provides a derivation of a known approximate analytical expression for this line in the temperature-density phase diagram. The paper's results give the first demonstration that the isomorph theory can be applied to systems like dense colloidal suspensions and strongly coupled dusty plasmas.Comment: 12 pages, 12 figure