Decoherence within a single atom

An “almost diagonal” reduced density matrix (in coordinate representation) is usually a result of environment induced decherence and is considered the sign of classical behavior. We show that the proton of a ground state hydrogen atom can indeed possess such a density matrix. This example demonstrates that the “almost diagonal” structure may be derived from an interaction with a low number of degrees of freedom which play the role of the environment. We also show that decoherence effects in our example can only be observed if the interaction with the measuring device is significantly faster than the interaction with the environment (the electron). In the opposite case, when the interaction with the environment is significant during the measurement process, coherence is maintained. Finally, we propose a neutron scattering experiment on cold He atoms to observe decoherence which shows up as an additional positive contribution to the differential scattering cross section. This contribution is inversely proportional to the bombarding energy.     

Protonation and Alkylation of Cross-conjugated Ketones Containing a Terminal N-Methylpyrrole Ring

The protonation and alkylation of cross-conjugated ketones containing a terminal N-methylpyrrole ring takes place at the oxygen atom. Protonation is accompanied by a strong bathochromic shift of the absorption maximum in the electron spectrum, while alkylation leads to ethoxypolymethine salts. The possibility of using these salts for the synthesis of ethoxycyanine dyes was studied.     

Complexes of Cobalt(II) and Zinc(II) with Heterocyclic Compounds Derived from 1,3-Indanedione

Complexes of Co(II) and Zn(II) with three-membered structures containing 1,3-indanedione, 1,3,4-thiadiazole, and pyridine moieties were obtained.     

Fullerene C6 0 Aggregates in Polymethyl Methacrylate Films

The structure of aggregates of fullerene C_{6 0} introduced into films of radical polymethyl methacrylate in the stage of solution preparation was studied by wide-angle X-ray diffraction.     

Characterization theorems for the projective space and vector bundle adjunction

 We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction. We use methods and techniques of the so called Mori theory, in particular the study of rational curves on projective manifolds. Received: 16 May 2002 / Revised version: 18 November 2002 Published online: 3 March 2003 Mathematics Subject Classification (2000): 14E30, 14J40, 14J45