Light-induced spin change by photodissociable external ligands: a new principle for magnetic switching of molecules

Magnetic bistability in spin-crossover materials generally is a collective phenomenon that arises from the cooperative interaction of a large number of microscopic magnetic moments within the crystal lattice in the solid state. We now report on individual molecules in homogeneous solution that are switched between the diamagnetic and paramagnetic states at room temperature by light-driven coordination-induced spin-state switching (LD-CISSS). Switching of the coordination number (and concurrently of the spin state) was achieved by using Ni-porphyrin as a square-planar platform and azopyridines as photodissociable axial ligands. The square-planar Ni-porphyrin is diamagnetic (low-spin, S = 0), and all complexes with axial ligands are paramagnetic (high-spin, S = 1). Association constants were determined for all conceivable 1:1 and 1:2 porphyrin/azopyridine complexes. The binding constants of the trans azopyridines are larger than those of the corresponding cis isomers. Thus, upon irradiation with UV light (365 nm, trans → cis) and visible light (455 nm, cis → trans), switching of the magnetic properties was achieved. Upon substitution of the azopyridines at the 4- and 4'-positions with larger substituents, the difference in trans and cis association constants, and thus the switching efficiency, was increased. A photoinduced, reversible switching between 20 and 68% paramagnetic Ni species in solution was achieved with isopropyl substituents at room temperature.     

Quantum Fields Obtained from Convoluted Generalized White Noise Never Have Positive Metric

It is proven that the relativistic quantum fields obtained from analytic continuation of convoluted generalized (Lévy type) noise fields have positive metric, if and only if the noise is Gaussian. This follows as an easy observation from a criterion by Baumann, based on the Dell’Antonio–Robinson–Greenberg theorem, for a relativistic quantum field in positive metric to be a free field.     

Generalizations of Heilbronn’s triangle problem

For given integers d,j≥2 and any positive integers n, distributions of n points in the d-dimensional unit cube [0,1]^d are investigated, where the minimum volume of the convex hull determined by j of these n points is large. In particular, for fixed integers d,k≥2 the existence of a configuration of n points in [0,1]^d is shown, such that, simultaneously for j=2,…,k, the volume of the convex hull of any j points among these n points is Ω(1/n^{(j−1)/(1+|d−j+1|)}). Moreover, a deterministic algorithm is given achieving this lower bound, provided that d+1≤j≤k.     

Combined approach of isotope mass balance and hydrological water balance methods to constrain the sources of lake water as exemplified on the small dimictic lake Silbersee,northern Germany

Stable isotopes of hydrogen and oxygen are often used for water balance calculations of lakes. We present an approach combining the lake water balance with an isotope mass balance to constrain the sources and sinks of the water of a small dimictic lake subjected to eutrophication. Meteorological and hydraulic data in combination with measured isotope signatures of the different water compartments enabled to assess the degree of surface water/groundwater interaction and the amount of overland flow into the lake. Groundwater could be excluded as a lake water source, as its water level was always below the lake water level. In the absence of a channelled inflow, precipitation and overland flow were the remaining options, whereby the latter was only active during periods of exceptionally high rainfall. While the groundwater signatures adjacent to the lake showed an influence of lake water, the lake water balance itself indicated that the associated volumetric water loss to groundwater is rather negligible. In the present case, only a combined assessment of hydrological and isotopic data allowed for an accurate characterization of the studied lake and a quantification of its water sources and sinks, highlighting the importance of using more than one methodological approach for such a purpose.     

An Indefinite Metric Model for Interacting Quantum Fields on Globally Hyperbolic Space-Times

We consider a relativistic ansatz for the vacuum expectation values (VEVs) of a quantum field on a globally hyperbolic space-time which is motivated by certain Euclidean field theories. The Yang-Feldman asymptotic condition w.r.t. an in-field in a quasi-free representation of the canonic commutation relations (CCR) leads to a solution of this ansatz for the VEVs. A GNS-like construction on a non-degenerate inner product space then gives local, covariant quantum fields with indefinite metric on a globally hyperbolic space-time. The non-trivial scattering behavior of quantum fields is analyzed by construction of the out-fields and calculation of the scattering matrix. A new combined effect of non-trivial quantum scattering and non-stationary gravitational forces is described for this model, as quasi-free in- fields are scattered to out-fields which form a non-quasi-free representations of the CCR. The asymptotic condition, on which the construction is based, is verified for the concrete example of de Sitter space-time. Communicated by Klaus Fredenhagen submitted 03/05/02, accepted: 18/07/03