The Born-Oppenheimer approach to the matter-gravity system is illustrated in a simple minisuperspace model and the corrections to quantum field theory on a semiclassical background exhibited. Within such a context the unitary evolution for matter, in the absence of phenomena such as tunnelling or other instabilities, is verified and compared with the results of other approaches. Lastly the simplifications associated with the use of adiabatic invariants to obtain the solution of the explicitly time dependent evolution equation for matter are evidenced. 0

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The method of adiabatic invariants for time dependent Hamiltonians is applied to a massive scalar field in a de Sitter space-time. The scalar field ground state, its Fock space and coherent states are constructed and related to the particle states. Diverse quantities of physical interest are illustrated, such as particle creation and the way a classical probability distribution emerges for the system at late times. *

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We present the ab initio results for the energetics of several SiC surfaces having different underlying bulk polytypes, to investigate the role of surface effects in the mechanisms of stacking inversion in SiC. We considered the Si adatom √3×√3 reconstruction for the cubic SiC(111) and the hexagonal SiC(0001) surfaces, taking into account the different subsurface bulk terminations compatible with the 4H and 6H polytypes, and allowing for two opposite stacking orientations of the topmost surface layer. Our investigation reveals that the energy differences among SiC polytypes are enhanced at the surface with respect to the bulk, and two-dimensional effects favor the formation of cubic SiC. We discuss the relevant role played by the surface energetics in the homoepitaxial growth of SiC

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Using cluster perturbation theory we calculate Greenʼs functions, quasi-particle energies and topological invariants for interacting electrons on a 2D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This allows us to define the parameter range (Hubbard U versus spinorbit coupling) where the 2D system behaves as a trivial insulator or quantum spin Hall insulator. This behavior is confirmed by the existence of gapless quasi-particle states in honeycomb ribbons. We have discussed the importance of the cluster symmetry and the effects of the lack of full translation symmetry typical of CPT and of most quantum cluster approaches. Comments on the limits of applicability of the method are also provided.

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