Energy Landscapes and Computer
Simulations
J. E. Gubernatis
Los Alamos National Laboratory
T-11, MS B262
Los Alamos, NM 87545
(505) 665-1167
(505) 665-4063 FAX
I would like to bring to the attention of the community several recent developments in computer simulation methods that facilitate the sampling of the energy landscape (EL) and offer new mechanisms for studying and interpreting a material's dynamics on this landscape.
All materials have energy landscapes. Modifying the phrase with various combinations of adjectives like smooth, rough, rugged, funneled, multi-basin, etc. sometimes provides a qualitative mechanism to partially describe differences between classes of materials like super-cooled liquids and proteins and to qualitatively explain some properties of these materials like slow dynamics and non-Arrhenius temperature dependencies.
Unfortunately, the greater "complexity" implied by the adjective usually transfers into the greater complexity required in performing a computer simulation of a CAM. In recent years, however, a wealth of new simulation methods has been proposed which address the needs of CAM. The Gibbs ensemble, hybrid Monte Carlo, multicanonical, and expanded ensemble methods are a several examples of techniques now being used to study various standard models of structural phase transitions and bead-spring models of biopolymer folding. When combined with massively parallel computers, these recent advances offer unprecedented opportunities to explore CAM.
Clouding this optimism is the often unheeded dictum of computational physics, "Garbage in, garbage out." I view this sobering warning is more of an opportunity than it is a difficulty. The simulations, or any analytic studies, of CAM models will only produce useful information in proportion to the utility of the models. The opportunity is for the triad of science -- experiment, theory, and simulation -- to work together to develop and refine the CAM models and the accompanying concepts.
What are core problems for CAM and ones for which the EL is an ingredient? Here are several general questions I ask myself: How useful is the concept of an order parameter in complex materials exhibiting intrinsic co-operative phenomena? Order parameters are often hidden and need not exist. Are similar but newer concepts need? What are the dynamics of the order parameters? Is there new dynamics? To what extent is the complex behavior of complex materials manifestations of (multiple) broken symmetries? Symmetries are clearly broken but some like replica symmetry are not obvious. What are the relevant symmetries? Are concepts of rigidity and topological defects (order parameter singularities) relevant and useful? Is there a place for long-range order? How does all the above change for large but intrinsically finite systems? For systems which are not self-averaging?