Stochastic Quantization of Bottomless Systems: Stationary quantities in a diffusive process

TL;DR

This paper investigates the stochastic quantization of bottomless systems using Langevin dynamics, demonstrating the existence of stationary quantities despite the absence of equilibrium in such divergent diffusive processes.

Contribution

It introduces a method to analyze stationary quantities in bottomless systems through stochastic quantization, extending understanding of their temporal behavior and initial condition dependence.

Findings

Stationary quantities can be identified in bottomless systems.

The initial conditions influence the temporal evolution of the process.

Divergent diffusive processes can exhibit stationary behavior.

Abstract

By making use of the Langevin equation with a kernel, it was shown that the Feynman measure exp(-S) can be realized in a restricted sense in a diffusive stochastic process, which diverges and has no equilibrium, for bottomless systems. In this paper, the dependence on the initial conditions and the temporal behavior are analyzed for 0-dim bottomless systems. Furthermore, it is shown that it is possible to find stationary quantities.