Casimir Force at a Finite Cut-Off

Abstract

We calculate the Casimir force at a finite cut-off Λ by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit LΛ → ∞. There is a correction in the order of (LΛ) −2 , when LΛ is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale Λ −1 . It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.

Casimir effect modified surface energy of a nanocavity in homogeneous media

“…It is well known that the van der Waals/Casimir energy and stress diverges in the spherical configurations . The divergence requires the regularization of the Casimir effects by either (1) imposing a length‐scale dependent cut‐off in the angular momentum , or (2) regularizing the expression by subtracting an “infinite” term corresponding to the bare surface tension of the liquid‐vacuum interface . A similar regularization procedure was imposed in the case of a perfect metal shell, and the corresponding and finite result was found to be repulsive .…”