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 u(th), 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 u(th) at a temperature close to the mode-coupling transition temperature T(c).

We applied a multicanonical algorithm to a two-dimensional and a three-dimensional Lennard-Jones system with quasicrystalline and glassy ground states. Focusing on the ability of the algorithm to locate low-lying energy states, we compared the results of the multicanonical simulations with standard Monte Carlo simulated annealing and molecular-dynamics methods. We find slight benefits to using multicanonical sampling in small systems ͑less than 80 particles͒, which disappear with larger systems. This is disappointing as the multicanonical methods are designed to surmount energy barriers to relaxation. We analyze this failure theoretically and show that ͑i͒ the multicanonical method is reduced in the thermodynamic limit ͑large systems͒ to an effective Monte Carlo simulated annealing with a random temperature vs time and ͑ii͒ the multicanonical method gets trapped by unphysical entropy barriers in the same metastable states whose energy barriers trap the traditional quenches. The performance of Monte Carlo and molecular-dynamics quenches were remarkably similar.

Abstract. -We study the distribution of overlaps of glassy minima, taking proper care of residual symmetries of the system. Ensembles of locally stable, low lying glassy states are efficiently generated by rapid cooling from the liquid phase which has been equilibrated at a temperature Trun. Varying Trun, we observe a transition from a regime where a broad range of states are sampled to a regime where the system is almost always trapped in a metastable glassy state. We do not observe any structure in the distribution of overlaps of glassy minima, but find only very weak correlations, comparable in size to those of two liquid configurations.The phenomenology of supercooled liquids, the glass transition and the glassy phase have been related to results of analytical calculations for microscopic models of spin glasses [1,2]. The latter bear no obvious relevance to structural glasses, hence, it is particularly important to see, whether the analogy can be supported quantitatively. One of the most prominent features of those spin-glass models, which have been put forward as models of structural glasses, is one step replica symmetry breaking, resulting in a bimodal distribution of overlaps between pure states. Generally speaking, one would expect to see non-trivial correlations among glassy states, if mean field theory of spin glasses were to apply.The liquid to glass transition as it is observed e.g. in metallic glasses, is a non-equilibrium phenomenon with the crystalline state being the true ground state. Glassy states are in general metastable states, sometimes called quasi-ergodic components, which are mutually inaccessible on experimental time scales, while equilibrium within a quasi-ergodic component is reached on much shorter time scales. In contrast to mean field models of spin glasses the ensemble of metastable states depends on the preparation method and the appropriate weights for metastable states are not unique. The assumption of an idealised preparation method, which cools the liquid arbitrarily slowly and at the same time prevents crystallization, has never been verified and seems contradictory to us. We therefore prefer to use a different idealised preparation ensemble which corresponds to infinitely rapid cooling from liquid equilibrium states. This method was first introduced by Stillinger and Weber [3,4]. Typeset using EURO-T E X

Abstract. By means of molecular dynamics simulations, we study the stationary points of the potential energy in a Lennard-Jones liquid, giving a purely geometric characterization of the energy landscape of the system. We find a linear relation between the degree of instability of the stationary points and their potential energy, and we locate the energy where the instability vanishes. This threshold energy marks the border between saddle-dominated and minima-dominated regions of the energy landscape. The temperature where the potential energy of the Stillinger-Weber minima becomes equal to the threshold energy turns out to be very close to the mode-coupling transition temperature T c .The low temperature dynamics of supercooled liquids and glasses is often put in relation with the geometric properties of the potential energy landscape of these systems. In particular, the presence of a large number of inequivalent glassy minima has stimulated many studies in the past [1][2][3][4][5]. More recently, the study of meanfield models of spin-glasses has strengthened the persuasion that the dynamical behaviour of glassy systems is deeply connected to the topology of the energy landscape [6]. Moreover, it has been shown that spin-glass systems exhibiting one-step replica symmetry breaking (1RSB) have many dynamical properties in common with fragile structural glasses [7], suggesting that 1RSB mean-field spinglasses and fragile glasses may have a similar energy landscape.In this context, crucial questions are: How to characterize the energy landscape of a glassy system? How to quantify the similarity of the energy landscape of fragile glasses and 1RSB spin-glasses? Although utterly relevant, the structure of minima of the potential energy is not enough: even at low temperatures, when activation is the only mechanism of diffusion in liquids, overcoming a barrier implies crossing a saddle of the potential energy. Furthermore, at higher temperatures the system spends more time around saddles than minima, hence the structure of unstable stationary points is important for understanding the crossover from a nonactivated to an activated dynamics upon cooling [8,9]. The statistical properties