Casimir Effect under Quasi-Periodic Boundary Condition Inspired by Nanotubes

Abstract

When one studies the Casimir effect, the periodic (anti-periodic) boundary condition is usually taken to mimic a periodic (anti-periodic) structure for a scalar field living in a flat space with a non-Euclidean topology. However, there could be an arbitrary phase difference between the value of the scalar field on one endpoint of the unit structure and that on the other endpoint, such as the structure of nanotubes. Then, in this paper, a periodic condition on the ends of the system with an additional phase factor, which is called the ``quasi-periodic" condition, is imposed to investigate the corresponding Casimir effect. And an attractive or repulsive Casimir force is found, whose properties depend on the phase angle value. Especially, the Casimir effect disappears when the phase angle takes a particular value. High dimensional space-time case is also investigated.

8 pages, 1 figure, accepted by MPLA

References in corpus (11)

• Casimir forces between arbitrary compact objects
• Casimir force on a piston
• Casimir pistons with hybrid boundary conditions
• Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on zeta function technique
• The Casimir force of Quantum Spring in the (D+1)-dimensional spacetime
• Quantum Spring from the Casimir Effect
• Casimir Pistons for Massive Scalar Fields
• Repulsive Casimir Force from Fractional Neumann Boundary Conditions
• Fermionic Casimir effect with helix boundary condition
• Casimir effect of massive vector fields
• Repulsive Casimir force between silicon dioxide and superconductor

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• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Equivalence of zeta function technique and Abel-Plana formula in regularizing the Casimir energy of hyper-rectangular cavities