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We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence of the Green function leads to non-perturbative results for the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by high-precision Monte-Carlo simulations of the Bose-Hubbard model. In addition, our Green’s function approach allows for calculating the excitation spectrum both for zero and finite temperature and for determining the effective masses of particles and holes.
was designed to produce electric power. Each part of the chain from uranium
mining to handling of the waste is linked to serious contamination risks,
however. Uranium mining is generally linked to local to regional contamination.
The fuel production also produces depleted uranium at a ratio of 1:7. The
reactors are operating under danger of accidents. Numerous minor accidents and
endless temporary shut-downs are occasionally mixed with disastrous accidents.
The Chernobyl (1986) and Fukushima (2011) accidents are notorious. The radioactive
contamination from those accidents is still incomprehensible and will keep serious destructions of the environment for centuries
to come. The handling of the high-level nuclear waste remains unsolved. Methods
proposed in Sweden, Finland and France seem likely to lead to disastrous
radioactive contaminations in the future. The only way out of this dilemma
seems to be a disposal where the waste, though effectively sealed-off in the
bedrock, remains accessible and controllable. At present, the “cost &
benefit” balance seems strongly tilted over to the “far too costly side”,