Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

Abstract

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension δ is within its allowed region.We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.

The Casimir Effect at Finite Temperature in a Six-Dimensional Vortex Scenario

“…The Casimir effect for parallel plates in the spacetime with extra compactified dimensions was discussed [28][29][30][31][32][33][34][35][36][37][38]. The distinct influence from the fractal additional compactified dimension can be exhibited in the Casimir effect for parallel plates [39,40]. The Casimir effect for the same system in the braneworld was also studied [41][42][43][44][45][46][47][48][49][50].…”