Department Angewandte Mathematik und Physik
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In this work we discuss a parameter σ on weighted k-element multisets of [n]={1,…,n}. The sums of weighted k-multisets are related to k-subsets, k-multisets, as well as special instances of truncated interpolated multiple zeta values. We study properties of this parameter using symbolic combinatorics. We rederive and extend certain identities for ζtn({m}k). Moreover, we introduce random variables on the k-element multisets and derive their distributions, as well as limit laws for k or n tending to infinity.
In the present work, using the recently introduced framework of local geometric deformations, special types of vector fields – so-called hidden Killing vector fields – are constructed, which solve the Killing equation not globally, but only locally, i.e. in local subregions of spacetime. Taking advantage of the fact that the vector fields coincide locally with Killing fields and therefore allow the consideration of integral laws that convert into exact physical conservation laws on local scales, balance laws in dynamical systems without global Killing symmetries are derived that mimic as closely as possible the conservation laws for energy and angular momentum of highly symmetric models. The utility of said balance laws is demonstrated by a concrete geometric example, namely a toy model for the binary merger of two extremal Reissner–Nordström black holes.
In this paper, using the quasilocal formalism of Brown and York, the flow of energy through a closed surface containing a gravitating physical system is calculated in a way that augments earlier results on the subject by Booth and Creighton. To this end, by performing a variation of the total gravitational Hamiltonian (bulk plus boundary part), it is shown that associated tidal heating and deformation effects generally are larger than expected. This is because the aforementioned variation leads to previously unrecognized correction terms, including a bulk-to-boundary inflow term that does not appear in the original calculation of the time derivative of the Brown-York energy and leads to corrective extensions of Einstein’s quadrupole formula in the large sphere limit.
It has recently been shown that matter-wave interferometry can be used to imprint a periodic nanostructure onto a molecular beam, which provides a highly sensitive tool for beam displacement measurements. Herein, we used this feature to measure electronic properties of provitamin A, vitamin E, and vitamin K1 in the gas phase for the first time. The shift of the matter-wave fringes in a static electric field encodes the molecular susceptibility and the time-averaged dynamic electric dipole moment. The dependence of the fringe pattern on the intensity of the central light-wave diffraction grating was used to determine the molecular optical polarizability. Comparison of our experimental findings with molecular dynamics simulations and density functional theory provides a rich picture of the electronic structures and dynamics of these biomolecules in the gas phase with β-carotene as a particularly interesting example.
Designing experiments which delocalize ever more complex and more massive particles requires a quantitative assessment of new interferometer configurations. Here, we introduce a figure of
merit which quantifies the difference between a genuine quantum interference pattern and a classical shadow and use it to compare a number of near-field interferometer schemes. This allows us to identify the most promising setups for future tests of the quantum superposition principle, and to discuss the perspectives of interferometry with complex molecules and clusters.