Constraints on stable equilibria with fluctuation-induced (Casimir) forces.
We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges and show that any arrangement in space is unstable to small perturbations in position. This extends Earnshaw's theorem for electrostatics by including thermal fluctuations of internal charges. Quantum fluctuations of the electromagnetic field are responsible for Casimir or van der Waals interactions. Neglecting permeabilities, we find that any equilibrium position of items subject to such forces is also unstable if the permittivities of all objects are higher or lower than that of the enveloping medium, the former being the generic case for ordinary materials in vacuum.
Rahi
Sahand Jamal
SJ
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Kardar
Mehran
M
Emig
Thorsten
T