Quantum Spring from the Casimir Effect

Abstract

The Casimir effect arises not only in the presence of material boundaries but also in space with nontrivial topology. In this paper, we choose a topology of the flat $(D+1)$-dimensional spacetime, which causes the helix boundary condition for a Hermitian massless scalar field. Especially, Casimir effect for a massless scalar field on the helix boundary condition is investigated in two and three dimensions by using the zeta function techniques. The Casimir force parallel to the axis of the helix behaves very much like the force on a spring that obeys the Hooke's law when the ratio $r$ of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so we would like to call it \textit{quantum spring}. When $r$ is large, this force behaves like the Newton's law of universal gravitation in the leading order. On the other hand, the force perpendicular to the axis decreases monotonously with the increasing of the ratio $r$. Both forces are attractive and their behaviors are the same in two and three dimensions.

6 pages, 7 figures, published in PLB

References in corpus (9)

• New Developments in the Casimir Effect
• Tests of new physics from precise measurements of the Casimir pressure between two gold-coated plates
• Casimir forces between arbitrary compact objects
• Casimir force on a piston
• Attractive Casimir Forces in a Closed Geometry
• Vacuum Polarization of Massless Spinor Field in Global Monopole Spacetime
• Casimir pistons with hybrid boundary conditions
• Rigorous proof of attractive nature for Casimir force of p-odd hypercube
• Casimir Pistons for Massive Scalar Fields

Cited by in corpus (11)

• The Casimir force of Quantum Spring in the (D+1)-dimensional spacetime
• Thermal Casimir effect for the scalar field in flat spacetime under a helix boundary condition
• Fermionic Casimir effect with helix boundary condition
• Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation
• Casimir Effect under Quasi-Periodic Boundary Condition Inspired by Nanotubes
• Casimir effect with a helix torus boundary condition
• Quantum Spring
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition
• Topological Casimir effect in models with helical compact dimensions
• Generalized Quantum Spring