Stochastic quantization versus the microcanonical ensemble: Getting the best of both worlds
Abstract
The aim of this paper is to shed further light on the relation between two non-standard formulations of field theory: stochastic quantization and the microcanonical ensemble. One involves a first-order (Langevin) differential equation in a fictitious "time", and the other a second-order ordinary differential equation. I analyze a scheme which is a particular example of a canonical ensemble, and which reduces to the old schemes in different limits. For a gaussian degree of freedom it turns out that the autocorrelation function in the new scheme undergoes damped harmonic motion, and the scheme is optimized (for numerical simulation) at critical damping. This is a clear improvement over the old limits, which correspond to maximal and zero damping. For non-gaussian systems I argue that the new proposal always represents a significant improvement over a Langevin simulation, and may even improve over the microcanonical method, in which case only a trivial code modification is required. A useful by-product of the discussion is a better estimate of systematic errors in microcanonical simulations.
- Publication:
-
Nuclear Physics B
- Pub Date:
- 1985
- DOI:
- 10.1016/0550-3213(85)90369-4
- Bibcode:
- 1985NuPhB.257..652D