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

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

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

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

Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture

In the framework of a random matrix description of chaotic quantum scattering the positions of $S-$matrix poles are given by complex eigenvalues $Z_i$ of an effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture on statistics of $Z_i$ for systems with broken time-reversal invariance and verify that it allows to reproduce statistical characteristics of Wigner time delays known from independent calculations. We analyze the ensuing two-point statistical measures as e.g. spectral form factor and the number variance. In addition we find the density of complex eigenvalues of real asymmetric matrices generalizing the recent result by Efetov\cite{Efnh}.Comment: 4 page

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.

High-efficiency freezing-induced loading of inorganic nanoparticles and proteins into micron- and submicron-sized porous particles

We demonstrate a novel approach to the controlled loading of inorganic nanoparticles and proteins into submicron- and micron-sized porous particles. The approach is based on freezing/thawing cycles, which lead to high loading densities. The process was tested for the inclusion of Au, magnetite nanoparticles, and bovine serum albumin in biocompatible vaterite carriers of micron and submicron sizes. The amounts of loaded nanoparticles or substances were adjusted by the number of freezing/thawing cycles. Our method afforded at least a three times higher loading of magnetite nanoparticles and a four times higher loading of protein for micron vaterite particles, in comparison with conventional methods such as adsorption and coprecipitation. The capsules loaded with magnetite nanoparticles by the freezing-induced loading method moved faster in a magnetic field gradient than did the capsules loaded by adsorption or coprecipitation. Our approach allows the preparation of multicomponent nanocomposite materials with designed properties such as remote control (e.g. via the application of an electromagnetic or acoustic field) and cargo unloading. Such materials could be used as multimodal contrast agents, drug delivery systems, and sensors

A New Seleukid Mint: Samarkand – Marakanda

The paper considers a group of four unique copper coins. These coins, representing a new type: crab / bee with the legend ‘King Antiochos’, were found between 2004 and 2012 at the site of Afrasiab – the ancient capital of Sogdiana (Marakanda) – and nearby. In the first publication of these coins, A. Atakhodzhaev attributed the coinage to the Seleukid king Antiochos III (223–187 B.C.) during his eastern campaign (c. 212–204 B.C.). The author argues that this coinage should instead be assigned to Antiochos I (ca. 295–281 B.C. – as co-ruler of the eastern satrapies, 281–261 B.C. – as sole ruler) or Antiochos II (261–246 B.C.). It is further postulated that the short-lived mint of Marakanda operated between c. 280 and 250 B.C