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Register a new userInhomogeneity-related cutoff dependence of the Casimir energy and stress
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The cutoff dependence of the Casimir energy and stress is studied using the Greens function method for a system that is piecewise-smoothly inhomogeneous along one dimension. The asymptotic cylinder kernel expansions of the energy and stress are obtained, with some extra cutoff terms that are induced by the inhomogeneity. Introducing interfaces to the system one by one shows how those cutoff terms emerge and illuminates their physical interpretations. Based on that, we propose a subtraction scheme to address the problem of the remaining cutoff dependence in the Casimir stress in an inhomogeneous medium, and show that the nontouching Casimir force between two separated bodies is cutoff independent. The cancellation of the electric and magnetic contributions to the surface divergence near a perfectly conducting wall is found to be incomplete in the case of inhomogeneity.
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This letter proposes a scheme for transporting nanoparticles immersed in a fluid, relying on quantum vacuum fluctuations. The mechanism lies in the inhomogeneity-induced lateral Casimir force between a nanoparticle and a gradient metasurface, and the relaxation of the conventional Dzyaloshinskiv{i}-Lifshitz-Pitaevskiv{i} constraint, which allows quantum levitation for a broader class of material configurations. The velocity for a nanosphere levitated above a grating is calculated and can be up to a few microns per minute. The Born approximation gives general expressions for the Casimir energy which reveal size-selective transport. For any given metasurface, a certain particle-metasurface separation exists where the transport velocity peaks, forming a Casimir passage. The sign and strength of the Casimir interactions can be tuned by the shapes of liquid-air menisci, potentially allowing real-time control of an otherwise passive force, and enabling interesting on-off or directional switching of the transport process.
Lateral Casimir force near a laterally-inhomogeneous plate is first revealed by both rigorous simulations and proximity approximations. The inhomogeneity-induced lateral Casimir force provides a novel method to control the lateral motion of nano-objects above the plate, and makes source-free manipulations of them possible. When incorporated with the Casimir repulsion in a fluid, the lateral Casimir force is shown to dominate over Brownian motion and enables long-distance quantum propulsion and firm quantum trapping of nano-objects. Gratings of varying filling factors to mimic micro-scale inhomogeneity also confirm those effects. The idea to design asymmetric distributions of nano-structures paves the way to sophisticated tailoring of the lateral Casimir force.
We present the vacuum of a two-dimensional conformal field theory (CFT$_2$) as a network of Wilson lines in $SL(2,mathbb{R}) times SL(2,mathbb{R})$ Chern-Simons theory, which is conventionally used to study gravity in three-dimensional anti-de Sitter space (AdS$_3$). The position and shape of the network encode the cutoff scale at which the ground state density operator is defined. A general argument suggests identifying the `density of complexity of this network with the extrinsic curvature of the cutoff surface in AdS$_3$, which by the Gauss-Bonnet theorem agrees with the holographic Complexity = Volume proposal.
The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitzs theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect.
We regard the Casimir energy of the universe as the main contribution to the cosmological constant. Using 5 dimensional models of the universe, the flat model and the warped one, we calculate Casimir energy. Introducing the new regularization, called {it sphere lattice regularization}, we solve the divergence problem. The regularization utilizes the closed-string configuration. We consider 4 different approaches: 1) restriction of the integral region (Randall-Schwartz), 2) method of 1) using the minimal area surfaces, 3) introducing the weight function, 4) {it generalized path-integral}. We claim the 5 dimensional field theories are quantized properly and all divergences are renormalized. At present, it is explicitly demonstrated in the numerical way, not in the analytical way. The renormalization-group function ($be$-function) is explicitly obtained. The renormalization-group flow of the cosmological constant is concretely obtained.
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