Lognormal-like statistics of a stochastic squeeze process.

Area of Science:

• Physics
• Statistical Mechanics
• Quantum Optics

Background:

• Stochastic processes are fundamental in describing physical systems.
• The lognormal distribution is often assumed for radial coordinates due to the central limit theorem.
• Existing approximations, like the quantum Zeno approximation, may oversimplify radial diffusion.

Purpose of the Study:

• To perform an exact analysis of a stochastic squeeze process.
• To determine the drift and diffusion coefficients for the logarithm of the radial coordinate.
• To investigate deviations from the standard lognormal description and common approximations.

Main Methods:

• Exact mathematical analysis of the stochastic squeeze process.
• Calculation of drift and diffusion coefficients for log(r).
• Examination of radial moments and distribution tails.

Main Results:

• The drift and diffusion of log(r) were precisely determined.
• Radial diffusion exhibits a nonmonotonic dependence on the ratio w/D, challenging the quantum Zeno approximation.
• The analysis revealed that far non-Gaussian tails of the log(r) distribution significantly influence radial moments.

Conclusions:

• The heuristic lognormal description is insufficient for this stochastic squeeze process.
• The radial diffusion is more complex than predicted by the quantum Zeno approximation.
• Accurate modeling requires considering the non-Gaussian nature of the radial coordinate distribution.