Fluctuation Pressure of a Membrane Between Walls Through Five Loops

TL;DR

This paper extends a calculation of the fluctuation pressure of a membrane between walls from four to five loops, using variational perturbation theory and comparisons with quantum mechanics to improve estimates, though results are above Monte Carlo data.

Contribution

It introduces a five-loop calculation of membrane fluctuation pressure and employs variational perturbation theory and quantum analogy for enhanced analysis.

Findings

Values exceed Monte Carlo data

Five-loop calculation improves previous estimates

Quantum analogy provides alternative pressure estimates

Abstract

An earlier four-loop calculation of the fluctuation pressure of a fluid membrane between two infinite walls is extended to five loops. Variational perturbation theory is used to extract the hard-wall limit from perturbative results obtained with a smooth potential. Comparison with a structurally similar quantum mechanics problem of a particle in a box is used for an alternative way of extracting the membrane pressure and also to estimate the quality of the results. Our values lie above the best available Monte Carlo data.