Hopping in a Supercooled Lennard-Jones Liquid: Metabasins, Waiting Time Distribution, and Diffusion

We investigate the jump motion among potential energy minima of a Lennard-Jones model glass former by extensive computer simulation. From the time series of minima energies, it becomes clear that the energy landscape is organized in superstructures, called metabasins. We show that diffusion can be pictured as a random walk among metabasins, and that the whole temperature dependence resides in the distribution of waiting times. The waiting time distribution exhibits algebraic decays: $\tau^{-1/2}$ for very short times and $\tau^{-\alpha}$ for longer times, where $\alpha\approx2$ near $T_c$. We demonstrate that solely the waiting times in the very stable basins account for the temperature dependence of the diffusion constant.Comment: to be published in Phys. Rev.

Relaxation dynamics of multi-level tunneling systems

A quantum mechanical treatment of an asymmetric double-well potential (DWP) interacting with a heat bath is presented for circumstances where the contribution of higher vibrational levels to the relaxation dynamics cannot be excluded from consideration. The deep quantum limit characterized by a discrete energy spectrum near the barrier top is considered. The investigation is motivated by simulations on a computer glass which show that the considered parameter regime is ``typical'' for DWPs being responsible for the relaxation peak of sound absorption in glasses. Relaxation dynamics resembling the spatial- and energy-diffusion-controlled limit of the classical Kramers' problem, and Arrhenius-like behavior is found under specific conditions.Comment: 23 pages, RevTex, 2 figures can be received from the Authors upon reques

How Cooperative are the Dynamics in Tunneling Systems? A Computer Study for an Atomic Model Glass

Via computer simulations of the standard binary Lennard-Jones glass former we have obtained in a systematic way a large set of close-by pairs of minima on the potential energy landscape, i.e. double-well potentials (DWP). We analyze this set of DWP in two directions. At low temperatures the symmetric DWP give rise to tunneling systems. We compare the resulting low-temperature anomalies with those, predicted by the standard tunneling model. Deviations can be traced back to the energy dependence of the relevant quantities like the number of tunneling systems. Furthermore we analyze the local structure around a DWP as well as the translational pattern during the transition between both minima. Local density anomalies are crucial for the formation of a tunneling system. Two very different kinds of tunneling systems are observed, depending on the type of atom (small or large) which forms the center of the tunneling system. In the first case the tunneling system can be interpreted as a single-particle motion, in the second case it is more collective

On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces

In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlying meshes are supposed to be quasi-uniform. We use \bH(\div)-conforming discretisations with quadrilateral elements of Raviart-Thomas type and establish quasi-optimal convergence of hp-approximations. Main ingredient of our analysis is a new \tilde\bH^{-1/2}(\div)-conforming p-interpolation operator that assumes only \bH^r\cap\tilde\bH^{-1/2}(\div)-regularity ($r>0$) and for which we show quasi-stability with respect to polynomial degrees