Instantons on Calabi–Yau cones

The Hermitian Yang–Mills equations on certain vector bundles over Calabi–Yau cones can be reduced to a set of matrix equations; in fact, these are Nahm-type equations. The latter can be analysed further by generalising arguments of Donaldson and Kronheimer used in the study of the original Nahm equations. Starting from certain equivariant connections, we show that the full set of instanton equations reduce, with a unique gauge transformation, to the holomorphicity condition alone.

The renormalization group via statistical inference

In physics, one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure to identify the corresponding equivalence classes of states, and argue that the renormalization group (RG) arises from the inherent ambiguities associated with the classes: one encounters flow parameters as, e.g., a regulator, a scale, or a measure of precision, which specify representatives in a given equivalence class. This provides a unifying framework and reveals the role played by information in renormalization. We validate this idea by showing that it justifies the use of low-momenta n-point functions as statistically relevant observables around a Gaussian hypothesis. These results enable the calculation of distinguishability in quantum field theory. Our methods also provide a way to extend renormalization techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the relationships between various type of RG.

Iron(III) Complexes on a Dendrimeric Basis and Various Amine Core Investigated by Mössbauer Spectroscopy

Dendrimers of various generations were synthesized by the divergent method. Starting from various amine cores (G(0a), G(0b), G(0c)) the generations were built by reaction of the amine with acrylnitrile followed by hydrogenation with DIBAL-H. Treatment with salicylaldehyde creates a fivefold coordination sphere for iron in the molecular periphery. The resulting multinuclear coordination compounds are investigated by Mossbauer spectroscopy.

Mössbauer Spectroscopic Study andMagnetic Investigation of Iron(III) Complexes on a DendrimericBasis

The functionalization of the molecular surface of various dendrimer generations with a phosphorous core and external amine groups is obtained by converting those amine groups into the corresponding imines of salicylaldehyde creating multiple coordination sites for the iron atoms. Treatment with iron(III) chloride yields multinuclear iron(III) complexes on a dendrimeric basis. The obtained multinuclear molecular systems exhibit extremely high total spin values. The influence of the generation growth on this type of coordination compounds is investigated by Mossbauer spectroscopy and SQUIDmagnetometry.

Equilibration of quantum gases

Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators.Weshow that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N, which is much faster than previous general upper bounds, which were exponential in N. For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one-dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists ofNfermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time O(1 N).