Markovian versus non-Markovian stochastic quantization of a complex-action model

Abstract

We analyze the Markovian and non-Markovian stochastic quantization methods for a complex action quantum mechanical model analog to a Maxwell-Chern-Simons eletrodynamics in Weyl gauge. We show through analytical methods convergence to the correct equilibrium state for both methods. Introduction of a memory kernel generates a non-Markovian process which has the effect of slowing down oscillations that arise in the Langevin-time evolution toward equilibrium of complex action problems. This feature of non-Markovian stochastic quantization might be beneficial in large scale numerical simulations of complex action field theories on a lattice.

Accepted for publication in the International Journal of Modern Physics A

References in corpus (13)

• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Lattice simulations of real-time quantum fields
• Adaptive stepsize and instabilities in complex Langevin dynamics
• Stochastic quantization at finite chemical potential
• Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
• Real-time gauge theory simulations from stochastic quantization with optimized updating
• On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential
• Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential
• Non-renormalizability of the HMC algorithm
• Stochastic Quantization for Complex Actions
• Stochastic Quantization of Topological Field Theory: Generalized Langevin Equation with Memory Kernel
• Stochastic Quantization of Real-Time Thermal Field Theory