Casimir force between integrable and chaotic pistons
Ezequiel Álvarez1, Francisco D. Mazzitelli1, Alejandro G. Monastra2, Diego A. Wisniacki1
Published under licence by PHYSICAL REVIEW A
1 Departamento de Física, Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires, and Instituto de Física de Buenos Aires, Concejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
2 Gerencia de Investigación y Aplicaciones, Comisión Nacional de Energía Atómica, Concejo Nacional de Investigaciones Científicas y Técnicas, Avenida General Paz 1499, 1650 San Martín, Argentina
Abstract
We have computed numerically the Casimir force between two identical pistons inside a very long cylinder, considering different shapes for the pistons. The pistons can be considered quantum billiards, whose spectrum determines the vacuum force. The smooth part of the spectrum fixes the force at short distances and depends only on geometric quantities like the area or perimeter of the piston. However, correcting terms to the force, coming from the oscillating part of the spectrum which is related to the classical dynamics of the billiard, could be qualitatively different for classically integrable or chaotic systems. We have performed a detailed numerical analysis of the corresponding Casimir force for pistons with regular and chaotic classical dynamics. For a family of stadium billiards, we have found that the correcting part of the Casimir force presents a sudden change in the transition from regular to chaotic geometries. This suggests that there could be signatures of quantum chaos in the Casimir effect.