Numerical and semiclassical analysis of some generalized Casimir pistons
- Department of Physics, Rutgers University, Newark, New Jersey 07102 (United States)
The Casimir force due to a scalar field in a cylinder of radius r with a spherical cap of radius R>r is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines the Casimir force. The spectral function of convex domains is obtained from a probability measure on convex surfaces that is induced by the Wiener measure on Brownian bridges the convex surfaces are the hulls of. Due to reflection positivity, the vacuum force on the piston by a scalar field satisfying Dirichlet boundary conditions is attractive in these geometries, but the strength and short-distance behavior of the force depend strongly on the shape of the piston casing. For a cylindrical casing with a hemispherical head, the force on the piston does not depend on the dimension of the casing at small piston elevation a<<R and numerically approaches F{sub cas}(a<<R)=-0.003 26(4)({Dirac_h}/2{pi})c/a{sup 2}. Semiclassically this asymptotic force is due to short, closed, and nonperiodic trajectories that reflect just once off the piston near its periphery. A semiclassical estimate reproduces the numerical results for the small-distance behavior of the force within statistical errors, whereas the proximity force approximation is off by one order of magnitude when R{approx}r.
- OSTI ID:
- 21300792
- Journal Information:
- Physical Review. A, Vol. 79, Issue 5; Other Information: DOI: 10.1103/PhysRevA.79.052105; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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