Roughness correction to the Casimir force : Beyond the Proximity Force Approximation

We calculate the roughness correction to the Casimir effect in the parallel plates geometry for metallic plates described by the plasma model. The calculation is perturbative in the roughness amplitude with arbitrary values for the plasma wavelength, the plate separation and the roughness correlation length. The correction is found to be always larger than the result obtained in the Proximity Force Approximation.Comment: 7 pages, 3 figures, v2 with minor change

Particle Creation by a Moving Boundary with Robin Boundary Condition

We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic moving boundary. We derive a Bogoliubov transformation between input and output bosonic field operators, which allows us to calculate the spectral distribution of created particles. The cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases. These two limits yield the same spectrum, which turns out to be an upper bound for the spectra derived for Robin BC. We show that the particle emission effect can be considerably reduced (with respect to the Dirichlet/Neumann case) by selecting a particular value for the oscillation frequency of the boundary position

Dynamical Casimir effect with cylindrical waveguides

I consider the quantum electromagnetic field in a coaxial cylindrical waveguide, such that the outer cylindrical surface has a time-dependent radius. The field propagates parallel to the axis, inside the annular region between the two cylindrical surfaces. When the mechanical frequency and the thickness of the annular region are small enough, only Transverse Electromagnetic (TEM) photons may be generated by the dynamical Casimir effect. The photon emission rate is calculated in this regime, and compared with the case of parallel plates in the limit of very short distances between the two cylindrical surfaces. The proximity force approximation holds for the transition matrix elements in this limit, but the emission rate scales quadratically with the mechanical frequency, as opposed to the cubic dependence for parallel plates.Comment: 6 page

Quantum radiation in a plane cavity with moving mirrors

We consider the electromagnetic vacuum field inside a perfect plane cavity with moving mirrors, in the nonrelativistic approximation. We show that low frequency photons are generated in pairs that satisfy simple properties associated to the plane geometry. We calculate the photon generation rates for each polarization as functions of the mechanical frequency by two independent methods: on one hand from the analysis of the boundary conditions for moving mirrors and with the aid of Green functions; and on the other hand by an effective Hamiltonian approach. The angular and frequency spectra are discrete, and emission rates for each allowed angular direction are obtained. We discuss the dependence of the generation rates on the cavity length and show that the effect is enhanced for short cavity lengths. We also compute the dissipative force on the moving mirrors and show that it is related to the total radiated energy as predicted by energy conservation.Comment: 17 pages, 1 figure, published in Physical Review

Inertial forces in the Casimir effect with two moving plates

We combine linear response theory and dimensional regularization in order to derive the dynamical Casimir force in the low frequency regime. We consider two parallel plates moving along the normal direction in $D-$dimensional space. We assume the free-space values for the mass of each plate to be known, and obtain finite, separation-dependent mass corrections resulting from the combined effect of the two plates. The global mass correction is proportional to the static Casimir energy, in agreement with Einstein's law of equivalence between mass and energy for stressed rigid bodies.Comment: 9 pages, 1 figure; title and abstract changed; to appear in Physical Review

Casimir torque between corrugated metallic plates

We consider two parallel corrugated plates and show that a Casimir torque arises when the corrugation directions are not aligned. We follow the scattering approach and calculate the Casimir energy up to second order in the corrugation amplitudes, taking into account nonspecular reflections, polarization mixing and the finite conductivity of the metals. We compare our results with the proximity force approximation, which overestimates the torque by a factor 2 when taking the conditions that optimize the effect. We argue that the Casimir torque could be measured for separation distances as large as 1 $\mu{\rm m}.$Comment: 7 pages, 3 figures, contribution to QFEXT07 proceeding