Abstract The extrema of the position-dependent spontaneous magnetization in a periodically layered two-dimensional Ising model are calculated exactly. Their asymptotic behaviour for infinite width of the surrounding homogeneous sublayer is given. The perturbations caused by the neighbouring sublayers on this extremum in a very thick sublayer are shown to be decoupled. Thus the asymptotic decay of the magnetization far from a single layer-shaped inhomogeneity can be inferred from the quoted asymptotics of an extremum, and it is found to be d-3/2exp (-d/ξ₁˂ where d is the distance to the inhomogeneity and ξ₁˂ the correlation length in the underlying homogeneous lattice. The connection of this decay law to the asymptotic decay of correlations is dicussed.
An extended Bose-Einstein condensate (BEC) in an optical lattice provides a kind of periodic dielectric and causes band gaps to occur in the spectrum of light propagating through it. We examine the question whether these band gaps can modify the spontaneous emission rate of atoms excited from the BEC, and whether they can lead to a self-stabilization of the BEC against spontaneous emission. We find that self-stabilization is not possible for BECs with a density in the order of 10 14 cm −3. However, the corresponding non-Markovian behavior produces significant effects in the decay of excited atoms even for a homogeneous BEC interacting with a weak laser beam. These effects are caused by the occurrence of an avoided crossing in the photon (or rather polariton) spectrum. We also predict a new channel for spontaneous decay which arises from an interference between periodically excited atoms and periodic photon modes. This new channel should also occur in ordinary periodic dielectrics. 1
The effect of random perturbation is investigated for a Hamiltonian with systematic degeneracies. It turns out that the influence of the degeneracies remains significant under perturbation. The model simulates quantized versions of classically chaotic systems in that the Fourier transform of the level density shows the characteristic lines which would be associated with the periods of periodic orbits if the system had a classical analogy. The decaying magnitude of the recurring lines is related to the spread of the probability distribution under the influence of perturbation of the degenerate levels.