energy of spherical shell
At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements. Bargmann-Michel-Telegdi equations, which describe the evolution of a temperature and chemical potential. This energy is called the "self-energy" of the charge distribution. The Casimir energy B is the total zero-point energy of the exact multipolar normal modes, minus that of empty space, minus the self-energy of the given amount of material at infinite dilution. Also, the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. C60). The quantum-electrodynamic binding energies B are determined perturbatively to order (nα)² for single macroscopic bodies (quasi-continua mimicking atomic solids) having the dispersive dielectric function ε(ω){1 + 4πnαΩ²/(Ω²-(ω²-i0)²}, as if each atom were an oscillator of frequency Ω, and n the number density of atoms (pairwise separations ρ). The Casimir energy for a conducting spherical shell of radius a is computed using a direct mode summation approach. for Studies in Theo. classical test particle Thus, the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. To order (nα)², but not beyond, the results for solid bodies lead directly to those for cavities of the same shape and size in otherwise unbounded material. Dispersion is incorporated by a plasma-like model. The rigorous finite-temperature QED formalism of the polarization tensor is used to study the combined effect of nonzero mass gap $m$ and chemical potential $\mu$ on the Casimir force and its thermal correction in the experimentally relevant configuration of a Au sphere interacting with a real graphene sheet or with graphene-coated dielectric substrates made of different materials. On the gravitational self-energy of a spherical shell Item Preview remove-circle Share or Embed This Item. eccentricity greater than ∼0.9 has a lower electrostatic energy than a spherical shell of the same area. It is shown that, in a strong static field, the nanotubes exhibit the negative differential conductivity. gravitational field characterized by curvature and torsion. Furthermore, computations show that the Casimir force is much stronger for graphene-coated substrates than for a free-standing graphene sample, but the thermal correction and its fractional weight in the total force are smaller in the former case. Then B is always dominated by terms of order stemming from TM modes; but the pattern of corrections as functions of x and X is intricate, and accessible only through the Debye (uniform) expansions of the Bessel functions figuring in the δl. The entropy is free of ultraviolet divergences and its calculation does not need any regularization. Box 19395-5531, Tehran, IRAN 2Department of Science, Physics group, Kordestan University, Sanandeg, Iran 3Department of Physics, Yarmouk University, Irbid-Jordan August 29, 2003 Realistically one has x 1, but μ ≡ 4πxX can be large or small. This region is at small values of temperature and plasma frequency (in units of the inverse radius). Abstract—Thin spherical shells usually fail due to buckling. To our surprise, for more singular configurations, as in the presence of sharp boundaries, the heat kernel coefficients behave to some extent better than in the corresponding smooth cases, making, for instance, the dilute dielectric ball a well-defined problem. We analyze the ultraviolet divergences in the ground state energy for a penetrable sphere and a dielectric ball. December 7, 2014. by Mini Physics. Physics and Mathematics(IPM) P. O. s-1) continuing until the final epoch (~1018Â s) of the universe to be integrated into a singular entity. These results are applied to a differential setup that was recently proposed to observe the giant thermal effect in the Casimir force for graphene. The most precise value proposed so far is CB = 0.046 1765; but the significance of comparisons is unclear, because previous calculations mistakenly treat the Boyer component as if it included all of B in a hypothetical perfect-reflector limit x → ∞.