Molecular Dynamics and Hybrid Monte Carlo
Molecular dynamics (MD) simulation is a deterministic procedure to integrate the equations of motion based on the classical mechanics principles (Hamiltonian equations). This method was first proposed by Alder and Wainwright (1959) and has become one of the most widely used research tools for complex physical systems. In a typical MD simulation study, one first sets up the quantitative system (model) of interest under a given condition (e.g., fixed number of particles and constant total energy). Then, successive configurations of the system, as a function of time, are generated by following Newton’s laws of motion. After a period of time for “equilibration,” one can start to collect “data” from this computer experiment — the data consist of a sequence of snapshots that record the positions and velocities of the particles in the system during a period of time. Based on these records, one can estimate “typical characteristics,” which can often be expressed as the time average of a function of the realized configurations, of the simulated physical system.
KeywordsMolecular Dynamic Simulation Hamiltonian Equation Stochastic Volatility Model Metropolis Algorithm Volume Preservation
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