Coherence and Uniqueness Theorems for Averaging Processes in Statistical Mechanics

Let S be the set of scalings {n ^–1:n=1,2,3,...} and let L _z =z Z ², zS, be the corresponding set of scaled lattices in R ². In this paper averaging operators are defined for plaquette functions on L _z to plaquette functions on L _z for all z, zS, z=dz, d{2,3,4,...}, and their coherence is proved. This generalizes the averaging operators introduced by Balaban and Federbush. There are such coherent families of averaging operators for any dimension D=1,2,3,... and not only for D=2. Finally there are uniqueness theorems saying that in a sense, besides a form of straightforward averaging, the weights used are the only ones that give coherent families of averaging operators.     

New effects in Young's interference experiment with partially coherent light

We analyze the coherence properties of a partially coherent optical field emerging from two pinholes in a plane opaque screen. We show that at certain pairs of points in the region of superposition the light is fully coherent, regardless of the state of coherence of the light at the pinholes. In particular, this result also holds if each pinhole is illuminated by a different laser.     

Zwicker tone illusion and noise reduction in the auditory system

The Zwicker tone is an auditory aftereffect. For instance, after switching off a broadband noise with a spectral gap, one perceives it as a lingering pure tone with the pitch in the gap. It is a unique illusion in that it cannot be explained by known properties of the auditory periphery alone. Here we introduce a neuronal model explaining the Zwicker tone. We show that a neuronal noise-reduction mechanism in conjunction with dominantly unilateral inhibition explains the effect. A pure tone's "hole burning" in noisy surroundings is given as an illustration.     

Dynamic and static conformational analysis of acylated tetrahydrobenzazepines

A detailed high-field NMR analysis of several acylated tetrahydrobenzazepines, supported by molecular mechanics calculations, indicates that the heterocyclic ring in these compounds exists in a chair conformation, with the carbonyl oriented anti to the aryl moiety in the dominant rotamer. Surprisingly, ring methylenes are typically diastereotopic at room temperature, as the barriers for the process of enantiomerization of the seven-membered ring are much higher than expected. It is shown that ring inversion is correlated (but not concerted) with rotation of the amide moiety, as the carbonyl is forced out of conjugation with the nitrogen in the transition state.