We study the dynamics of semiflexible dendritic polymers following the method of Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)]. The scheme allows to formulate in analytical form the corresponding Langevin equations. We determine the eigenvalues by first block-diagonalizing the problem, which allows to treat even very large dendritic objects. A basic ingredient of the procedure is the observation that a set of eigenmodes in the semiflexible case is similar to that chosen by Cai and Chen [Macromolecules 30, 5104 (1997)] for fully flexible dendritic structures. Varying the flexibility of the macromolecules allows us to better understand their mechanical loss moduli G"(ω) based on their eigenvalue spectra. We present the G"(ω) for a series of stiffness parameters and for different functionalities of the branching points.

We study the dynamics of semiflexible Vicsek fractals (SVF) following the framework established by Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)], a scheme which allows to model semiflexible treelike polymers of arbitrary architecture. We show, extending the methods used in the treatment of semiflexible dendrimers by Fürstenberg et al. [J. Chem. Phys. 136, 154904 (2012)], that in this way the Langevin-dynamics of SVF can be treated to a large part analytically. For this we show for arbitrary Vicsek fractals (VF) how to construct complete sets of eigenvectors; these reduce considerably the diagonalization problem of the corresponding equations of motion. In fact, such eigenvector sets arise naturally from a hierarchical procedure which follows the iterative construction of the VF. We use the obtained eigenvalues to calculate the loss moduli G(")(ω) of SVF for different degrees of stiffness of the junctions. Finally, we compare the results for SVF to those found for semiflexible dendrimers.

We consider an SU(2)-lattice gauge model in the tree gauge. Classically, this is a system with symmetries whose configuration space is a direct product of copies of SU(2), acted upon by diagonal inner automorphisms. We derive defining relations for the orbit type strata in the reduced classical phase space. The latter is realized as a certain quotient of a direct product of copies of the complexified group SL(2, C) (sometimes named the GITquotient because it provides a categorical quotient in the sense of geometric invariant theory). The relations derived can be used for the construction of the orbit type costratification of the Hilbert space of the quantum system in the sense of Huebschmann.

We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation forms of the complex dielectric susceptibility. We show that the dynamic behavior of single segments depends on their remoteness from the periphery rather than on the size of the whole macromolecule. Remarkably, the dynamics of the core segments (which are most remote from the periphery) shows a scaling behavior that differs from the dynamics obtained after structural average. We analyze the most relevant processes of single segment motion and provide an analytic approximation for the corresponding relaxation times. Furthermore, we describe an iterative method to calculate the orientational dynamics in the case of very large macromolecular sizes.

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