Collective Coordinate Control of Density Distributions

Real collective density variables $C(\boldsymbol{k})$ [c.f. Eq.\ref{Equation3})] in many-particle systems arise from non-linear transformations of particle positions, and determine the structure factor $S(\boldsymbol{k})$, where $\bf k$ denotes the wave vector. Our objective is to prescribe $C({\boldsymbol k})$ and then to find many-particle configurations that correspond to such a target $C({\bf k})$ using a numerical optimization technique. Numerical results reported here extend earlier one- and two-dimensional studies to include three dimensions. In addition, they demonstrate the capacity to control $S(\boldsymbol{k})$ in the neighborhood of $|\boldsymbol{k}| =$ 0. The optimization method employed generates multi-particle configurations for which $S(\boldsymbol{k}) \propto |\boldsymbol{k}|^{\alpha}$, $|\boldsymbol{k}| \leq K$, and $\alpha =$ 1, 2, 4, 6, 8, and 10. The case $\alpha =$ 1 is relevant for the Harrison-Zeldovich model of the early universe, for superfluid $^{4}{He}$, and for jammed amorphous sphere packings. The analysis also provides specific examples of interaction potentials whose classical ground state are configurationally degenerate and disordered.Comment: 26 pages, 8 figure

Perturbation theory for the effective diffusion constant in a medium of random scatterer

We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style

Scaling behavior in the β\beta-relaxation regime of a supercooled Lennard-Jones mixture

We report the results of a molecular dynamics simulation of a supercooled binary Lennard-Jones mixture. By plotting the self intermediate scattering functions vs. rescaled time, we find a master curve in the $\beta$-relaxation regime. This master curve can be fitted well by a power-law for almost three decades in rescaled time and the scaling time, or relaxation time, has a power-law dependence on temperature. Thus the predictions of mode-coupling-theory on the existence of a von Schweidler law are found to hold for this system; moreover, the exponents in these two power-laws are very close to satisfying the exponent relationship predicted by the mode-coupling-theory. At low temperatures, the diffusion constants also show a power-law behavior with the same critical temperature. However, the exponent for diffusion differs from that of the relaxation time, a result that is in disagreement with the theory.Comment: 8 pages, RevTex, four postscript figures available on request, MZ-Physics-10

Kinetic Heterogeneities in a Highly Supercooled Liquid

We study a highly supercooled two-dimensional fluid mixture via molecular dynamics simulation. We follow bond breakage events among particle pairs, which occur on the scale of the $\alpha$ relaxation time $\tau_{\alpha}$. Large scale heterogeneities analogous to the critical fluctuations in Ising systems are found in the spatial distribution of bonds which are broken in a time interval with a width of order $0.05\tau_{\alpha}$. The structure factor of the broken bond density is well approximated by the Ornstein-Zernike form. The correlation length is of order $100 \sigma_1$ at the lowest temperature studied, $\sigma_1$ being the particle size. The weakly bonded regions thus identified evolve in time with strong spatial correlations.Comment: 3 pages, 6 figure

Glassy Transition and Aging in a Model without Disorder

We study the off-equilibrium relaxational dynamics of the Amit-Roginsky $\phi^3$ field theory, for which the mode coupling approximation is exact. We show that complex phenomena such as aging and ergodicity breaking are present at low temperature, similarly to what is found in long range spin glasses. This is a generalization of mode coupling theory of the structural glass transition to off-equilibrium situations.Comment: 9 pages, 1 uuencoded figure, LaTex, preprint NORDITA 94/3

Phase diagram of glassy systems in an external field

We study the mean-field phase diagram of glassy systems in a field pointing in the direction of a metastable state. We find competition among a ``magnetized'' and a ``disordered'' phase, that are separated by a coexistence line as in ordinary first order phase transitions. The coexistence line terminates in a critical point, which in principle can be observed in numerical simulations of glassy models.Comment: 4 pages, 5 figure

Geometric approach to the dynamic glass transition

We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by a qualitative change in the topological properties of the landscape. Furthermore, we show that the potential energy barriers connecting local glassy minima increase with decreasing energy of the minima, and we relate this behaviour to the fragility of the system. Finally, we analyze the real space structure of activated processes by studying the distribution of particle displacements for local minima connected by simple saddles

Computer investigation of the energy landscape of amorphous silica

The multidimensional topography of the collective potential energy function of a so-called strong glass former (silica) is analyzed by means of classical molecular dynamics calculations. Features qualitatively similar to those of fragile glasses are recovered at high temperatures : in particular an intrinsic characteristic temperature $T_c\simeq 3500$K is evidenced above which the system starts to investigate non-harmonic potential energy basins. It is shown that the anharmonicities are essentially characterized by a roughness appearing in the potential energy valleys explored by the system for temperatures above $T_c$.Comment: 5 pages; accepted for publication in PR

Apparent finite-size effects in the dynamics of supercooled liquids

Molecular dynamics simulations are performed for a supercooled simple liquid with changing the system size from N=108 to $10^4$ to examine possible finite-size effects. Although almost no systematic deviation is detected in the static pair correlation functions, it is demonstrated that the structural $\alpha$ relaxation in a small system becomes considerably slower than that in larger systems for temperatures below $T_c$ at which the size of the cooperative particle motions becomes comparable to the unit cell length of the small system. The discrepancy increases with decreasing temperature.Comment: 4 pages 5 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