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

M. E. S. Borelli·H. Kleinert·Adriaan M. J. Schakel
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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.

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M. E. S. Borelli, H. Kleinert, Adriaan M. J. Schakel. 2000-03-22. Quantum Statistical Mechanics of Nonrelativistic Membranes: Crumpling Transition at Finite Temperature. https://doi.org/10.1016/s0375-9601(00)00051-7

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