Result: Measuring the local geometry of valleys in complex energy landscapes by exhaustive exploration: The Lid method

Knowing the shape of the valleys in complex energy landscapes bears on a number of fields, ranging from the design of stochastic optimization algorithms, such as simulated annealing, to the study of thermal relaxation of glassy systems and to the prediction of metastable compounds for chemical synthesis. The 'lid' algorithm is designed to exhaustively explore the neighborhoods of local energy minima of model systems, extracting the features which are relevant for the dynamics. In this paper the algorithm is presented and some implementation issues, including those of parallel performance and scalability, are discussed. In addition, we present selected results pertaining to different models. These results are chosen to illustrate the versatility of the method and to highlight the important traits, e.g. the exponential nature of the dependence of the local density of states on the energy and of the local state space volume on the energy barrier, which are shared by a wide range of applications. The implications for the relaxation behavior and the thermal metastability of the systems considered are briefly discussed.