Convergence of path measures arising from a mean field or polaron type interaction

Summary We discuss the limiting path measures of Markov processes with either a mean field or a polaron type interaction of the paths. In the polaron type situation the strength is decaying at large distances on the time axis, and so the interaction is of short range in time. In contrast, in the mean field model, the interaction is weak, but of long range in time. Donsker and Varadhan proved that for the partition functions, there is a transition from the polaron type to the mean field interaction when passing to a limit by letting the strength tend to zero while increasing the range. The discussion of the path measures is more subtle. We treat the mean field case as an example of a differentiable interaction and discuss the transition from the polaron type to the mean field interaction for two instructive examples.Research supported by the Swiss National Foundation (21-29833.90)This article was processed by the authors using the Springer-Verlag T_EX ProbTh macro package 1991.     

Über die Einwirkung von Ammoniak auf Anthragallol

Ohne ZusammenfassungDiese Untersuchung ist vor mehr als Jahresfrist infolge Eintrittes in die chemische Praxis abgebrochen worden. Äussere Verhältnisse machen die Vollendung der begonnenen Versuche auch weiterhin unmöglich und sehe ich mich desshalb veranlasst, meine Beobachtungen zu veröffentlichen.     

Maximum-entropy data analysis

The reconstruction of physical quantities from (computer-) experimental data is very often hampered by the presence of noise, insufficient information and above all by the ill-posed nature of the underlying inversion problem. It will be demonstrated that the maximum entropy concepts is particularly suited for this type of data-analysis problems. It is based on Bayesian statistics and provides a consistent probabilistic theory to obtain unbiased results, independent of any model assumptions. This is particularly desirable if there is no additional information to justify these hypotheses. If, on the other hand, additional prior knowledge is available, it can be effectively incorporated into the computation, leading to more stringent confidence intervals.     

Diffusive motion of iron microcrystals studied by Mössbauer spectroscopy

A new model is presented which explains well the dramatic decrease of the Mössbauer line intensities with raising temperatures for freely dispersed iron microscrystals. In contrast to other theories which consider mainly vibration to be responsible we discuss here the decrease in terms of large amplitude diffusive rotational or translational jumps of the particles. Such diffusive jumps lead — in agreement with the observation — to a strong reduction of the Mössbauer-intensity without broadening the line width in a noticeable way. The typical potential well for a diffusing particle in an equilibrium position is derived quantitatively to be 13 meV. The model might be important also for a new understanding of the dynamics of catalytic clusters either in contact with each other or with larger solid surfaces.Part of this work was supported by the DFG Sonderforschungsbereich 306, Konstanz     

Common luminescence intensity fluctuations of single particle and single molecules in non-conducing matrices

Optical spectroscopy in combination with wide field or confocal optical microscopy enables the investigation of single quantum objects such as organic molecules, II/VI semiconductor quantum dots and silicon nanocrystals. They all have fluctuations of luminescence intensities on time scales longer than μs in common. A comparison reveals that despite the large differences of the nature of the respective quantum objects, the intensity fluctuations are related to a slow ionisation process followed by a trapping of the photoejected charge in the non-conducing environment. Detailed aspects of the dynamics are controlled by the dielectric properties of the matrix.