We consider a quantum-mechanical analysis of spontaneous emission in terms of an effective twolevel system with a vacuum decay rate Γ0 and transition angular frequency ωA. Our analysis is in principle exact, even though presented as a numerical solution of the time-evolution including memory effects. The results so obtained are confronted with previous discussions in the literature. In terms of the dimensionless lifetime τ = tΓ0 of spontaneous emission, we obtain deviations from exponential decay of the form O(1/τ ) for the decay amplitude as well as the previously obtained asymptotic behaviors of the form O(1/τ 2 ) or O(1/τ ln 2 τ ) for τ ≫ 1. The actual asymptotic behavior depends on the adopted regularization procedure as well as on the physical parameters at hand. We show that for any reasonable range of τ and for a sufficiently large value of the required angular frequency cut-off ωc of the electro-magnetic fluctuations, i.e. ωc ≫ ωA, one obtains either a O(1/τ ) or a O(1/τ 2 ) dependence. In the presence of physical boundaries, which can change the decay rate with many orders of magnitude, the conclusions remains the same after a suitable rescaling of parameters.

We consider the energy shift for an atom close to a non-magnetic body with a magnetic moment coupled to a quantized magnetic field. The corresponding repulsive Casimir-Polder force is obtained for a perfect conductor, a metal, a dielectric medium, with dielectric properties modeled by a Drude formula, and a superconductor at zero temperature. The dielectric properties of the superconductor is obtained by making use of the Mattis-Bardeen linear response theory and we present some useful expressions for the low-frequency conductivity. The quantum dynamics with a given initial state is discussed in terms of the well-known Weisskopf-Wigner theory and is compared with corresponding results for a electric dipole coupling. The results obtained are compatible with a conventional master equation approach. In order to illustrate the dependence on geometry and material properties, numerical results are presented for the ground state using a two-level approximation.

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