Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on a zeta function technique

2014

Mod. Phys. Lett. A

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.

Section: Introductionmentioning

confidence: 99%

Casimir Effect Under Quasi-Periodic Boundary Condition Inspired by Nanotubes

Feng

2014

Mod. Phys. Lett. A

“…is considered in M D+1 with the induced topology and define an equivalence relation ∼ on X by 36) where T = 3, · · · , D. Then the anti-helix conditions imposed on a field ψ,…”

Section: The Vacuum Energy Density For a Fermion Fieldmentioning

confidence: 99%

Some developments of the Casimir effect in p-cavity of (D + 1)-dimensional space–time

Lin

Feng

et al. 2014

Int. J. Mod. Phys. A

The Casimir effect for rectangular boxes has been studied for several decades. But there are still some points unclear. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization methods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the p-dimensional cavity in (D + 1)-dimensional spacetime, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity.

“…57 In fact, for homogeneous Epstein zeta function eq. (2.4), consider Z D (D − s), which is well-defined for s < 0, …”

Section: Generalization To Higher Dimensional Casesmentioning

confidence: 99%

Equivalence of zeta function technique and Abel–Plana formula in regularizing the Casimir energy of hyper-rectangular cavities

Lin

2014

Mod. Phys. Lett. A

Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic continuation. By contrast, Abel-Plana formula method permits explicit separation of divergent terms. In regularizing the Casimir energy for a massless scalar field in a D-dimensional rectangular box, we give the rigorous proof of the equivalence of the two methods by deriving the reflection formula of Epstein zeta function from repeatedly application of Abel-plana formula and giving the physical interpretation of the infinite integrals. Our study may help with the confidence of choosing any regularization method at convenience among the frequently used ones, especially the zeta function method, without the doubts of physical meanings or mathematical consistency.