Rigorous proof of the attractive nature for the Casimir force of a<i>p</i>-odd hypercube

Li, Xinzhou; Zhai, Xiang-Hua

doi:10.1088/0305-4470/34/49/320

Cited by 20 publications

(19 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now we just have to collect them all and integrate them over k z as indicated in Eq. (15). The integral of the three different kind of branch cuts can be easily calculated and the results for each are: The sum over j in the last equation comes from the Taylor expansion of the denominator of that particular branch-cut term Eq.…”

Section: Appendix a Electromagnetic Modes In Waveguidesmentioning

confidence: 99%

A direct approach to the electromagnetic Casimir energy in a rectangular waveguide

Valuyan

Moazzemi

Gousheh

2008

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

In this paper we compute the leading order Casimir energy for the electromagnetic field (EM) in an open ended perfectly conducting rectangular waveguide in three spatial dimensions by a direct approach. For this purpose we first obtain the second quantized expression for the EM field with boundary conditions which would be appropriate for a waveguide. We then obtain the Casimir energy by two different procedures. Our main approach does not contain any analytic continuation techniques. The second approach involves the routine zeta function regularization along with some analytic continuation techniques. Our two approaches yield identical results. This energy has been calculated previously for the EM field in a rectangular waveguide using an indirect approach invoking analogies between EM fields and massless scalar fields, and using complicated analytic continuation techniques, and the results are identical to ours. We have also calculated the pressures on different sides and the total Casimir energy per unit length, and plotted these quantities as a function of the cross-sectional dimensions of the waveguide. We also present a physical discussion about the rather peculiar effect of the change in the sign of the pressures as a function of the shape of the cross-sectional area.

show abstract

Section: Appendix a Electromagnetic Modes In Waveguidesmentioning

confidence: 99%

A direct approach to the electromagnetic Casimir energy in a rectangular waveguide

Valuyan

Moazzemi

Gousheh

2008

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

show abstract

“…Inevitably a lot of attention has been focused on the role of boundary conditions and very recently on the interplay of material properties, temperature, and geometry. Some new methods have developed for computing the Casimir effect between a finite number of compact objects [8], inside a rectangular box or cavity [10][11][12]. When a topology of the flat spacetime was chosen to cause the helix boundary condition for a scalar field, the Casimir force behaves very much like the force on a spring that obeys the Hooke's law when the ratio of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so the author call it quantum spring [13] [14] or quantum anti-spring [15] corresponding to periodic-like and anti-periodic-like boundary condition, see also [16].…”

Section: Introductionmentioning

confidence: 99%

Casimir Effect Under Quasi-Periodic Boundary Condition Inspired by Nanotubes

Feng

Zhai

2014

Mod. Phys. Lett. A

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…So, the regularized temperaturedependent parts of the free energy densities for these two BCs are 27) where the sign "+" corresponds to Dirichlet BCs and the sign "−" to Neumann BCs. It is obvious that the term proportional to T 4 is the blackbody radiation energy restricted in the volume L 3 , regardless of the BCs.…”

Section: Dirichlet and Neumann Bcsmentioning

confidence: 99%

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

Zhai

Lin

Feng

et al. 2014

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Rigorous proof of the attractive nature for the Casimir force of ap-odd hypercube

Cited by 20 publications

References 12 publications

A direct approach to the electromagnetic Casimir energy in a rectangular waveguide

A direct approach to the electromagnetic Casimir energy in a rectangular waveguide

Casimir Effect Under Quasi-Periodic Boundary Condition Inspired by Nanotubes

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

Contact Info

Product

Resources

About