Generalized Quantum Spring

Abstract

Recently, it was found that after imposing a helix boundary condition on a scalar field, the Casimir force coming from the quantum effect is linearly proportional to $r$, which is the ratio of the pitch to the circumference of the helix. This linear behavior of the Casimir force is just like that of the force obeying the Hooke's law on a spring. In this paper, inspiring by some complex structures that lives in the cells of human body like DNA, protein, collagen etc., we generalize the helix boundary condition to a more general one, in which the helix consists of a tiny helix structure, and makes up a hierarchy of helix. After imposing this kind of boundary condition on a massless and a massive scalar, we calculate the Casimir energy and force by using the so-called zeta function regularization method. We find that the Hooke's law with the generalized helix boundary condition is not exactly the same as usual one. In this case, the force is proportional to the cube of $r$ instead. So we regard it as a generalized Hooke's law, which is complied by a \emph{generalized quantum spring}.

10 pages, 1 figure

References in corpus (12)

• Casimir forces between arbitrary compact objects
• Casimir force on a piston
• Casimir pistons with hybrid boundary conditions
• The perfect magnetic conductor (PMC) Casimir piston in d+1 dimensions
• Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston
• The Casimir force of Quantum Spring in the (D+1)-dimensional spacetime
• Casimir Pistons for Massive Scalar Fields
• Quantum Spring from the Casimir Effect
• Repulsive Casimir Force from Fractional Neumann Boundary Conditions
• Fermionic Casimir effect with helix boundary condition
• Casimir effect of massive vector fields
• Quantum Spring