Time evolution with symmetric stochastic action

作     者：Peter D. Drummond 

作者机构：Centre for Quantum and Optical Science Swinburne University of Technology Melbourne 3122 Australia Institute of Theoretical Atomic Molecular and Optical Physics (ITAMP) Harvard University Cambridge 02138 MA United States Weizmann Institute of Science Rehovot 7610001 Israel 

出 版 物：《Physical Review Research》 (Phys. Rev. Res.)

年 卷 期：2021年第3卷第1期

页      面：013240-013240页

核心收录：

基　　金：Australian Research Council  ARC  (DP190101480) 

主　　题：Bose-Einstein condensates Path integrals Quantum field theory Heatbath algorithm Quantum Monte Carlo Quantum theory 

摘      要：The time evolution of quantum fields is shown to be equivalent to a time-symmetric Fokker-Planck equation. Results are obtained using a Q-function representation, including fermion-fermion, boson-boson, and fermion-boson interactions with linear, quadratic, cubic, and quartic Hamiltonians, typical of QED and many other cases. For local boson-boson coupling, the resulting probability distribution is proved to have a positive, time-symmetric path integral and action principle, leading to a forward-backward stochastic process in both time directions. The solution corresponds to a c-number field equilibrating in an additional dimension. Paths are stochastic trajectories of fields in space-time, which are samples of a statistical mechanical steady state in a higher-dimensional space. We derive numerical methods and examples of solutions to the resulting stochastic partial differential equations in a higher time dimension, giving agreement with examples of simple bosonic quantum dynamics. This approach may lead to useful computational techniques for quantum field theory, as well as to new ontological models of physical reality.