论文标题
广义量子弹簧
Generalized Quantum Spring
论文作者
论文摘要
最近，发现在标量场上施加了螺旋边界条件后，来自量子效应的Casimir力与$ r $成正比，这是螺距与螺旋的圆周的比率。卡西米尔力量的这种线性行为就像在春天服从胡克定律的力量一样。在本文中，通过某些复杂的结构启发，这些结构生活在人体细胞中，例如DNA，蛋白质，胶原蛋白等，我们将螺旋边界条件推广到更一般的边界条件，其中螺旋由很小的螺旋结构组成，并构成了螺旋的层次结构。在将这种边界条件施加在无质量和大规模标量上后，我们使用所谓的zeta函数正则化方法来计算Casimir的能量和力。我们发现，具有广义螺旋边界条件的胡克定律与往常并不完全相同。在这种情况下，部队与$ r $的立方体成正比。因此，我们将其视为普遍的胡克定律，该定律由\ emph {generalized Quantum Spring}遵守。
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}.
