Integrals of monomials over the orthogonal group

A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is expressible as a finite sum of partial fractions in $N$. The recursion formula largely extends presently available integration formulas for the orthogonal group.Comment: 9 pages, no figure

Universal model for exoergic bimolecular reactions and inelastic processes

From a rigorous multichannel quantum-defect formulation of bimolecular processes, we derive a fully quantal and analytic model for the total rate of exoergic bimolecular reactions and/or inelastic processes that is applicable over a wide range of temperatures including the ultracold regime. The theory establishes a connection between the ultracold chemistry and the regular chemistry by showing that the same theory that gives the quantum threshold behavior agrees with the classical Gorin model at higher temperatures. In between, it predicts that the rates for identical bosonic molecules and distinguishable molecules would first decrease with temperature outside of the Wigner threshold region, before rising after a minimum is reached.Comment: 5 pages, 1 figur

A trivial observation on time reversal in random matrix theory

It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is time reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models.Comment: 7 pages 3 figure

Occurrence of photosynthetic microbial mats in a Lower Cretaceous black shale (central Italy): a shallow-water deposit

Cretaceous oceanic anoxic events (OAEs) were periods of high organic carbon burial corresponding to intervals with excellent organic matter (OM) preservation. This work focuses on the Urbino level, i.e., OAE1b, which is thought to be of regional extent. A detailed microscopical study of OM shows a dominance of microbial activity, characterized by a typical arrangement of exopolymeric substances (EPS) related to microbial mats, bacterial bodies, and some photosynthetic microorganisms, as shown by thylakoids. The latter lived where they have been found, i.e., at the sea bottom, which indicates that OM results from the diagenesis of benthic photosynthetic microbial mats, an interpretation supported through the comparison with a recent analogue. The exceptional preservation of such organic structures in OM points to the joint role of the selective and sorptive preservation pathways. These data and interpretation strongly differ from previous observations in OAE1b equivalents. They suggest that the Urbino level might be an atypical OAE of regional/local extent which was formed within the photic zon

The permeability of dead plant cells for some enzymes

The penetration of α-chymotrypsin and/or pancreatic lipase into dead cells of soybean cotyledons, of yeast and of algae was studied using the enzymic activity as a parameter. In addition a fluorescent antibody technique was applied for the localization of α-chymotrypsin within the soybean cells.The digestibility of unheated, EDTA-treated substrate was similar to that of the heated substrate. Since EDTA-treatment increases the permeability of the cell wall and cell membrane of the plant cell without denaturing proteins contained in the cells, we concluded that heating affected mainly the barrier formed by the cell wall, thus permitting a better passage of big molecules (enzymes).Leakage of β-amylase (mol. weight 61,700) from soybean occurred only after treatment with EDTA. This confirmed that EDTA enhances the permeability of the cell wall.α-Chymotrypsin (mol. weight 24,000) and pancreatic lipase (mol. weight 38,000) penetrated unheated sections, whereas amylopectin (mol. weight 50,000-1,000,000) did not penetrate unheated cotyledons. Apparently the greater dimension of amylopectin compared with α-chymotrypsin and lipase accounts for its lack of entry into unheated soybean cotyledons. However, when we applied the fluorescent antibody technique to localize α-chymotrypsin within the cells from unheated sections, we used antibodies (γ-globulins) having a mol. weight of 150,000. They entered the unheated sections and produced a positive result of the experiment. Consequently the size of the molecules as indicated by the molecular weight, is not the reason why amylopectin did not penetrate the unheated cotyledons. Moreover, this shows that α-chymotrypsin probably opens a way for the entry of globulins. Therefore the entry of proteolytic enzymes is not an inert process. This is conceivable as the enzymes are big molecules with catalytic activity.Unheated non-EDTA-treated soybean (with plasmodesmata) was slightly penetrated by α-chymotrypsin, whereas unheated non-EDTA-treated yeast and algae (both without plasmodesmata) were not penetrated at all. Furthermore, in soybean material (unheated or heated) α-chymotrypsin enhanced the penetration of lipase; this effect was absent in the case of yeast. The results obtained strongly suggest that plasmodesmata are a way in dead plant cells for penetration of enzymes

Non-local model of hollow cathode and glow discharge - theory calculations and experiment comparison

General form of the non-local equation for an ionization source in glow discharge and hollow cathode 3D-simulation is formulated. It is a fundamental equation in a hollow cathode theory, which allows to make up a complete set of field equations for a self-consistent problem in a stationary glow discharge and a hollow cathode. It enables to describe adequately the region of negative glow and the hollow cathode effect. Here you can see first attempts to compare calculation results of electrical dependences (pressure - voltage) and experimental data, - under conditions of gradual appearance of the hollow cathode effect.Comment: 4 pages, 2 figure

Performance of Hamamatsu 64-anode photomultipliers for use with wavelength--shifting optical fibres

Hamamatsu R5900-00-M64 and R7600-00-M64 photomultiplier tubes will be used with wavelength--shifting optical fibres to read out scintillator strips in the MINOS near detector. We report on measurements of the gain, efficiency, linearity, crosstalk, and dark noise of 232 of these PMTs, of which 219 met MINOS requirements.Comment: 15 pages, 12 figures. Accepted by Nucl. Inst. Meth.

Fidelity and level correlations in the transition from regularity to chaos

Mean fidelity amplitude and parametric energy--energy correlations are calculated exactly for a regular system, which is subject to a chaotic random perturbation. It turns out that in this particular case under the average both quantities are identical. The result is compared with the susceptibility of chaotic systems against random perturbations. Regular systems are more susceptible against random perturbations than chaotic ones.Comment: 7 pages, 1 figur

Quantum chaotic system as a model of decohering environment

As a model of decohering environment, we show that quantum chaotic system behave equivalently as many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic environment is derived. This theoretical formulation is substantiated by the numerical study of decoherence of two qubits interacting with a quantum chaotic environment modeled by a chaotic kicked top. Like the many-body model of environment, the quantum chaotic system is efficient decoherer, and it can generate entanglement between the two qubits which have no direct interaction.Comment: 5 pages, 3 figures. Published version