Stochastic Variational Approach to Minimum Uncertainty States

TL;DR

This paper presents a novel variational framework for identifying minimum uncertainty states in Gaussian diffusion processes, extending to non-harmonic potentials through a constrained variational approach.

Contribution

It introduces a new variational characterization of Gaussian diffusion processes and develops a method to find minimum uncertainty states beyond harmonic potentials.

Findings

New variational characterization of Gaussian diffusion processes

Method for minimum uncertainty states in non-harmonic potentials

Extension of Schrödinger dynamics constraints

Abstract

We introduce a new variational characterization of Gaussian diffusion processes as minimum uncertainty states. We then define a variational method constrained by kinematics of diffusions and Schr\"{o}dinger dynamics to seek states of local minimum uncertainty for general non-harmonic potentials.