Robin Boundary Condition for Casimir Plates in a General Weak Gravitational Field

Abstract

The energy of the massless scalar field inside parallel Casimir plates in a general weak gravitational field under the influence of Robin boundary conditions is calculated. The mode frequencies are found in asymptotic limits and consistency of results with the literature is shown. Experimental evidence for detection of corrections is explored. Finding Mode Frequencies Inside the Plates for Robin Boundary ConditionsThe problem is to find mode frequencies of a scalar Klein-Gordon field inside an apparatus consisting of two conducting parallel plates in a general weak gravitational field under the influence of the Robin boundary conditions. The spacetime is dsecribed by the common spherical r, θ, φ coordinates. The plates are in a

Quantum vacuum under mixed boundary conditions: the case for curved spacetime

“…Fortunately, they made a significant improvment in measurement of the force between two microscopic masses at most four orders of magnitude better than existing data, i.e. δE E 0 ∼ 10 −6 [3] .…”

“…For a typical spacetime, say the Earth, ∼ 10 −10 near the surface of the Earth. An experimental investigation of Casimir force has been made in [3] using recent data obtained by employing the so-called Casimir-less technique developed by Chen et al [35]. Fortunately, they made a significant improvment in measurement of the force between two microscopic masses at most four orders of magnitude better than existing data, i.e.…”

“…Although there are still four orders of magnitudes needed to the disired level of accuracy to detect the shift of the energy, this improvement and underlying techniques in recent researches invokes the hopes for better measurement of the Casimir force in the near future [3,35]. , and the solid one the whole .…”

“…For material boundaries, the Robin coefficients play the role of skin depth of the surface [3]. Without having a physical boundary, a periodic boundary condition on a quantum field may also occur when the spacetime admits some compact dimensions [1,2].…”

Quantum Information Measures of the One‐Dimensional Robin Quantum Well

“…Structures with Robin BC are ubiquitous in nature. A correct understanding of the processes taking place in acoustics, electrodynamics, plasma, scalar field theory with special attention to the Casimir effect, superconductivity where the coefficient Λ is called the de Gennes distance, and other branches of physics and related fields inevitably requires finding solutions of the wave equation in the form of Equation with the additional requirement from Equation due to the confining surface. A continuous variation of the extrapolation length from its zero magnitude to the extremely large positive values smoothly transforms the BC from the Dirichlet to the Neumann case what has its consequences, for example, in the change of the sign of the Casimir force between two parallel plates .…”