Average characteristic polynomials in the two-matrix model

The two-matrix model is defined on pairs of Hermitian matrices $(M_1,M_2)$ of size $n\times n$ by the probability measure $$\frac{1}{Z_n} \exp\left(\textrm{Tr} (-V(M_1)-W(M_2)+\tau M_1M_2)\right)\ dM_1\ dM_2,$$ where $V$ and $W$ are given potential functions and \tau\in\er. We study averages of products and ratios of characteristic polynomials in the two-matrix model, where both matrices $M_1$ and $M_2$ may appear in a combined way in both numerator and denominator. We obtain determinantal expressions for such averages. The determinants are constructed from several building blocks: the biorthogonal polynomials $p_n(x)$ and $q_n(y)$ associated to the two-matrix model; certain transformed functions $\P_n(w)$ and \Q_n(v); and finally Cauchy-type transforms of the four Eynard-Mehta kernels $K_{1,1}$, $K_{1,2}$, $K_{2,1}$ and $K_{2,2}$. In this way we generalize known results for the $1$-matrix model. Our results also imply a new proof of the Eynard-Mehta theorem for correlation functions in the two-matrix model, and they lead to a generating function for averages of products of traces.Comment: 28 pages, references adde

Survival of Clostridium perfringens During Simulated Transport and Stability of Some Plasmid-borne Toxin Genes under Aerobic Conditions

Clostridium perfringens is a pathogen of great concern in veterinary medicine, because it causes enteric diseases and different types of toxaemias in domesticated animals. It is important that bacteria in tissue samples, which have been collected in the field, survive and for the classification of C. perfringens into the correct toxin group, it is crucial that plasmid-borne genes are not lost during transportation or in the diagnostic laboratory. The objectives of this study were to investigate the survival of C. perfringens in a simulated transport of field samples and to determine the stability of the plasmid-borne toxin genes cpb1 and etx after storage at room temperature and at 4°C. Stability of the plasmid-borne genes cpb1 and etx of C. perfringens CCUG 2035, and cpb2 from C. perfringens CIP 106526, JF 2255 and 6 field isolates in aerobic atmosphere was also studied. Survival of C. perfringens was similar in all experiments. The cpb1 and etx genes were detected in all isolates from samples stored either at room temperature or at 4°C for 24–44 h. Repeated aerobic treatment of C. perfringens CCUG 2035 and CIP 106526 did not result in the loss of the plasmid-borne genes cpb1, cpb2 or etx. Plasmid-borne genes in C. perfringens were found to be more stable than generally reported. Therefore, C. perfringens toxinotyping by PCR can be performed reliably, as the risk of plasmid loss seems to be a minor problem

On the stability of quantum holonomic gates

We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the adiabatic evolution but can reduce the logical gate performance. Using the intrinsic geometric properties of the holonomic gates, we show under which conditions on noise's correlation time and strength, the fluctuations in the driving field cancel out. In this way, we provide theoretical support to previous numerical simulations. We also briefly comment on the error due to the mismatch between real and nominal time of the period of the driving fields and show that it can be reduced by suitably increasing the adiabatic time.Comment: 7 page

Oscillator Strengths and Damping Constants for Atomic Lines in the J and H Bands

We have built a line list in the near-infrared J and H bands (1.00-1.34, 1.49-1.80 um) by gathering a series of laboratory and computed line lists. Oscillator strengths and damping constants were computed or obtained by fitting the solar spectrum. The line list presented in this paper is, to our knowledge, the most complete one now available, and supersedes previous lists.Comment: Accepted, Astrophysical Journal Supplement, tentatively scheduled for the Sep. 1999 Vol. 124 #1 issue. Text and tables also available at http://www.iagusp.usp.br/~jorge

Spatial distribution of low-energy plasma around 2 comet 67P/CG from Rosetta measurements

International audienceWe use measurements from the Rosetta plasma consortium (RPC) Langmuir probe (LAP) and mutual impedance probe (MIP) to study the spatial distribution of low-energy plasma in the near-nucleus coma of comet 67P/Churyumov-Gerasimenko. The spatial distribution is highly structured with the highest density in the summer hemisphere and above the region connecting the two main lobes of the comet, i.e. the neck region. There is a clear correlation with the neutral density and the plasma to neutral density ratio is found to be ∼1-2·10 −6 , at a cometocentric distance of 10 km and at 3.1 AU from the sun. A clear 6.2 h modulation of the plasma is seen as the neck is exposed twice per rotation. The electron density of the collisonless plasma within 260 km from the nucleus falls of with radial distance as ∼1/r. The spatial structure indicates that local ionization of neutral gas is the dominant source of low-energy plasma around the comet

Gibbs Ensembles of Nonintersecting Paths

We consider a family of determinantal random point processes on the two-dimensional lattice and prove that members of our family can be interpreted as a kind of Gibbs ensembles of nonintersecting paths. Examples include probability measures on lozenge and domino tilings of the plane, some of which are non-translation-invariant. The correlation kernels of our processes can be viewed as extensions of the discrete sine kernel, and we show that the Gibbs property is a consequence of simple linear relations satisfied by these kernels. The processes depend on infinitely many parameters, which are closely related to parametrization of totally positive Toeplitz matrices.Comment: 6 figure