Factorizing coupled quantum systems and damped nonlinear Schrödinger equations

We show that the wave function of a coupled quantum system may factorize for certain coupling operators, resulting in wave functions and effective nonlinear Hamiltonians for the subsystems. Systems of coupled harmonic oscillators with discrete or continuous spectra are considered, where all degrees of freedom move in time-dependent coherent Glauber states.We present the general formalism and study two examples in detail. The problem of radiation damping results under drastic assumptions in exponentially damped harmonic motion, obeying a nonlinear Schrödinger equation. In the second example, a different type of coupling is studied which yields inverse power law damping.     

New inflation in supersymmetric theories

A new inflationary universe scenario is considered based upon phase transitions in supersymmetric unified models where the Higgs potential is of the Witten-O'Raifeartaigh type.     

Studies on the Thorpe-Ziegler-reaction. A new synthesis of the pyridine part of thiamine]

Thorpe-Ziegler cyclization of N′-cyano-N-(2-cyanoethyl)-acetamidine ( 5a ) yields 4-amino-2-methyl-1,6-dihydro-5-pyrimidinecarbonitrile ( 8a ). The acetamidine 5a is accessible either from the N-cyanoimidate 1 and β-aminopropionitrile ( 3a ) or the N-cyanoamidine 2 and acrylonitrile ( 4 ). The dihydropyrimidine 8a is easily converted to 4-amino-2-methyl-5-pyrimidine-carbonitrile ( 13 ) by dehydrogenation or to 4-amino-5-aminomethyl-2-methylpyrimidine ( 15 ) by hydrogenation-dehydrogenation. Both products are important intermediates in the synthesis of thiamine.     

Measurement of the electric form factor of the neutron at Q2 = 0.3-0.8 (GeV/ c) 2 ⋆

The electric form factor of the neutron, G_E,n, has been measured at the Mainz Microtron by recoil polarimetry in the quasielastic D(¯e, e¯n)p reaction. Three data points have been extracted at squared four-momentum transfers Q ² = 0.3, 0.6 and 0.8 (GeV/c)². Corrections for nuclear binding effects have been applied.This revised version was published online in March 2005. In the previous version, the email address of one author was inadvertently assigned to multiple authors.     

Synthesis of 4,5-benzotropones by cyclization of 1,3-bis-silyl enol ethers with 1,2-dialdehydes

The cyclization of 1,3-bis-silyl enol ethers or (2,4-dioxobutylidene)triphenylphosphoranes with phthalic dialdehyde allowed a convenient synthesis of a variety of 4,5-benzotropones. The hydrogenation of benzotropones afforded functionalized benzocycloheptanones which were transformed into tricyclic butenolides.     

On a universal differential equation for the analytic terms of C-superpositions on the real line

It is proved that every continuous function on the real line can be approximated uniformly (in the sense of a specific norm) by superpositions of analytic functions, which are solutions of a single universal differential equation. Every superposition is some function belonging to . This improves a former result of the author, from which the superpositions are known to be continuous.     

Photoelectron imaging of helium droplets

The photoionization and photoelectron spectroscopy of He nanodroplets (10(4) atoms) has been studied by photoelectron imaging with photon energies from 22.5-24.5 eV. Total electron yield measurements reveal broad features, whose onset is approximately 1.5 eV below the ionization potential of atomic He. The photoelectron spectra are dominated by very low energy electrons, with less than 0.6 meV. These results are attributed to the formation and autoionization of highly vibrationally excited He(*)(n) Rydberg states within the cluster, followed by strong final state interactions between the photoelectron and the droplet.