Quantum Statistical Mechanics of Nonrelativistic Membranes: Crumpling Transition at Finite Temperature

TL;DR

This paper investigates how quantum fluctuations influence the behavior of nonrelativistic membranes, revealing that they stiffen the membrane and lead to a crumpling transition at finite temperature, contrasting thermal fluctuation effects.

Contribution

It provides a first-order perturbative renormalization group analysis showing quantum fluctuations stiffen membranes and identifies a crumpling transition at finite temperature.

Findings

Quantum fluctuations stiffen the membrane, maintaining a Hausdorff dimension of two.

Thermal fluctuations soften the membrane, leading to crumpling.

A nontrivial fixed point indicates a crumpling transition at finite temperature.

Abstract

The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to {\em stiffen} the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.