Casimir Forces between Beads on Strings and Membranes

Abstract

We develop a general formalism to calculate the force between beads attached to a flat $d$-dimensional membrane due to the quantum fluctuations of the membrane. The interaction potential is derived as a function of $d$ and the membrane energy density, tension, stiffness and temperature. We find that the induced interactions turn off when $d$ exceeds a certain critical dimension. The potential is attractive in all cases where it is non-zero and at finite temperature falls off exponentially for large distances.

Plain Tex, Tables.tex macro required, 9 pages

References in corpus (2)

• Wiggly Relativistic Strings
• Casimir forces between beads on strings

Cited by in corpus (5)

• The `Friction' of Vacuum, and other Fluctuation-Induced Forces
• Casimir Effect: The Classical Limit
• On the Casimir energy for a 2N-piece relativistic string
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• Casimir-like corrections to the classical tensions of the strings and membranes