Diffusion Processes and Coherent States

TL;DR

This paper demonstrates that diffusion processes inherently have uncertainty relations and can generate coherent and squeezed states, leading to new quantum states in time-dependent and damped oscillators using Nelson's stochastic quantum mechanics.

Contribution

It introduces a general framework linking diffusion processes to quantum coherent states and derives new minimum uncertainty states for complex oscillator models.

Findings

Diffusion processes exhibit uncertainty relations and coherent states.

Nelson's stochastic formulation can produce quantum states in various oscillator models.

New minimum uncertainty states are derived for time-dependent and damped oscillators.

Abstract

It is shown that stochastic processes of diffusion type possess, in all generality, a structure of uncertainty relations and of coherent and squeezed states. This fact is used to obtain, via Nelson stochastic formulation of quantum mechanics, the harmonic-oscillator coherent and squeezed states. The method allows to derive new minimum uncertainty states in time-dependent oscillator potentials and for the Caldirola-Kanai model of quantum damped oscillator.