Until now there exists no calculation of the phonon density of states of amorphous SiO, and related materials, which could interpret the experimentally detected splittings between longitudinal and transverse modes in their optical phonon spectra. This problem is solved by taking into account the influence of the vibrationally induced polarization on the motion of atoms. A simple model for the description of this polarization in non-crystalline SiO, is developed and used for the calculation of t h e density of states of LO and TO phonons in the framework of a coherent potential approximation for structurally disordered systems. This new method leads also to the determination of the I R response function and to simple analytical expressions for the microscopic parameters of the model, i.e. the bond angle at the oxygen atom and transverse dynamic effective charges. The values of these parameters are determined from I R transmission spectra of thin SiO, layers prepared with the help of different methods. The calculated density of states and I R response function are in good agreement with corresponding experimental results.

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The dual form of the massless Schwinger model on the lattice overcomes the complex action problems from two sources: a topological term, as well as non-zero chemical potential, making these physically interesting cases accessible to Monte Carlo simulations. The partition function is represented as a sum over fermion loops, dimers and plaquette-surfaces such that all contributions are real and positive. However, these new variables constitute a highly constrained system and suitable update strategies have to be developed. In this exploratory study we present an approach based on locally growing plaquette-surfaces surrounded by fermion loop segments combined with a worm based strategy for updating chains of dimers, as well as winding fermion loops. The update strategy is checked with conventional simulations as well as reference data from exact summation on small volumes and we discuss some physical implications of the results.

Dedicat.ed to Prof. Dr. E. GUTSCHE on the occasion of his 60th birthday It will be demonstrated that the so-called LO-TO splittings in the infrared spectra of thin amorphous insulating layers are a consequence of boundary conditions. Es wird gezeigt, daB die sogenannten LO-TO-Aufspaltungen in IR-Spektren dunner amorphcrIsolatorschichten aus Randbedingungen folgen.

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