Products of Random Matrices

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted prior in statistical image analysis.Comment: 9 pages, 1 figur

Ethane steam reforming over a platinum/alumina catalyst: effect of sulphur poisoning

In this study we have examined the adsorption of hydrogen sulfide and methanethiol over platinum catalysts and examined the effect of these poisons on the steam reforming of ethane. Adsorption of hydrogen sulfide was measured at 293 and 873 K. At 873 K the adsorbed state of hydrogen sulfide in the presence of hydrogen was SH rather than S, even though the Pt:S ratio was unity. The effect of 11.2 ppm hydrogen sulfide or methanethiol on the steam reforming of ethane was studied at 873 K and 20 barg. Both poisons deactivated the catalyst over a number of hours, but methanethiol was found to be more deleterious, reducing the conversion by almost an order of magnitude, possibly due to the co-deposition of sulfur and carbon. Changes in the selectivity revealed that the effect of sulfur was not uniform on the reactions occurring, with the production of methane reduced proportionally more than the other products, due to the surface sensitivity of the hydrogenolysis and methanation reactions. The water-gas shift reaction was affected to a lesser extent. No regeneration was observed when hydrogen sulfide was removed from the feedstream in agreement with adsorption studies. A slight regeneration was observed when methanethiol was removed from the feed, but this was believed to be due to the removal of carbon rather than sulfur. The overall effect of sulfur poisoning was to reduce activity and enhance hydrogen selectivity

Creation of Entanglement by Interaction with a Common Heat Bath

I show that entanglement between two qubits can be generated if the two qubits interact with a common heat bath in thermal equilibrium, but do not interact directly with each other. In most situations the entanglement is created for a very short time after the interaction with the heat bath is switched on, but depending on system, coupling, and heat bath, the entanglement may persist for arbitrarily long times. This mechanism sheds new light on the creation of entanglement. A particular example of two quantum dots in a closed cavity is discussed, where the heat bath is given by the blackbody radiation.Comment: 4 revtex pages, 1 eps figure; replaced with published version; short discussion on entanglement distillation adde

The Refractive Index of Silicon at Gamma Ray Energies

The index of refraction n(E_{\gamma})=1+\delta(E_{\gamma})+i\beta(E_{\gamma}) is split into a real part \delta and an absorptive part \beta. The absorptive part has the three well-known contributions to the cross section \sigma_{abs}: the photo effect, the Compton effect and the pair creation, but there is also the inelastic Delbr\"uck scattering. Second-order elastic scattering cross sections \sigma_{sca} with Rayleigh scattering (virtual photo effect), virtual Compton effect and Delbr\"uck scattering (virtual pair creation) can be calculated by integrals of the Kramers-Kronig dispersion relations from the cross section \sigma_{abs}. The real elastic scattering amplitudes are proportional to the refractive indices \delta_{photo}, \delta_{Compton} and \delta_{pair}. While for X-rays the negative \delta_{photo} dominates, we show for the first time experimentally and theoretically that the positive \delta_{pair} dominates for \gamma rays, opening a new era of \gamma optics applications, i.e. of nuclear photonics.Comment: 4 pages, 3 figure

Loss of Spin Entanglement For Accelerated Electrons in Electric and Magnetic Fields

Using an open quantum system we calculate the time dependence of the concurrence between two maximally entangled electron spins with one accelerated uniformly in the presence of a constant magnetic field and the other at rest and isolated from fields. We find at high Rindler temperature the proper time for the entanglement to be extinguished is proportional to the inverse of the acceleration cubed.Comment: 10 pages, 4 figures, appendix and other discussion added, fixed some typographical errors and some references were correcte

Dialogue Concerning Two Views on Quantum Coherence: Factist and Fictionist

A controversy that has arisen many times over in disparate contexts is whether quantum coherences between eigenstates of certain quantities are fact or fiction. We present a pedagogical introduction to the debate in the form of a hypothetical dialogue between proponents from each of the two camps: a factist and a fictionist. A resolution of the debate can be achieved, we argue, by recognizing that quantum states do not only contain information about the intrinsic properties of a system but about its extrinsic properties as well, that is, about its relation to other systems external to it. Specifically, the coherent quantum state of the factist is the appropriate description of the relation of the system to one reference frame, while the incoherent quantum state of the fictionist is the appropriate description of the relation of the system to another, uncorrelated, reference frame. The two views, we conclude, are alternative but equally valid paradigms of description.Comment: 14 pages, Contribution to the Int. J. of Quant. Info. issue dedicated to the memory of Asher Peres; v2 updated summary and critique of prior literatur

A surface electrode point Paul trap

We present a model as well as experimental results for a surface electrode radio-frequency Paul trap that has a circular electrode geometry well-suited for trapping of single ions and two-dimensional planar ion crystals. The trap design is compatible with microfabrication and offers a simple method by which the height of the trapped ions above the surface may be changed \emph{in situ}. We demonstrate trapping of single and few Sr+ ions over an ion height range of 200-1000 microns for several hours under Doppler laser cooling, and use these to characterize the trap, finding good agreement with our model.Comment: 10 pages, 11 figures, 1 tabl

Multiplying unitary random matrices - universality and spectral properties

In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a hamiltonian random in time. We find that the result is universal and depends only on the second moment of the generator of the stochastic evolution. We find indications of critical behavior (eigenvalue spacing scaling like $1/N^{3/4}$) close to $\theta=\pi$ for a specific critical evolution time $t_c$.Comment: 12 pages, 2 figure

Coherent Excitation of a Two-Level Atom driven by a far off-resonant Classical Field: Analytical Solutions

We present an analytical treatment of coherent excitation of a Two-Level Atom driven by a far-off resonant classical field. A class of pulse envelope is obtained for which this problem is exactly solvable. The solutions are given in terms of Heun function which is a generalization of the Hypergeometric function. The degeneracy of Heun to Hypergeometric equation can give all the exactly solvable pulse shapes of Gauss Hypergeometric form, from the generalized pulse shape obtained here. We discuss the application of the results obtained to the generation of XUV.Comment: 9 Pages, 8 Figures. Accepted for Physical Review A as a regular articl

Increased exposure to acute thermal stress is associated with a non-linear increase in recombination frequency and an independent linear decrease in fitness in Drosophila

Abstract Background Meiotic recombination rate has long been known to be phenotypically plastic. How plastic recombination evolves and is maintained remains controversial; though a leading model for the evolution of plastic recombination rests on the tenet that organismal fitness and recombination frequency are negatively correlated. Motivated by the mounting evidence that meiotic recombination frequencies increase in response to stress, here we test for a negative correlation between fitness and recombination frequency. Specifically, the fitness-associated recombination model (FAR) predicts that if stress increases meiotic recombination frequency, then increasing exposure to stressful conditions will yield an increasing magnitude of the recombinational response, while concomitantly decreasing fitness. Results We use heat shock as a stressor to test this prediction in Drosophila melanogaster. We find that increased exposure to heat shock conditions is associated with a non-linear increase in meiotic recombination frequency. We also find an independent effect of heat shock on organismal fitness, with fitness decreasing with increased duration of thermal stress. Conclusions Our results thus support the foundation of the FAR model for the evolution of plastic recombination. Our data also suggest that modulating recombination frequency is one mechanism by which organisms can rapidly respond to environmental cues and confer increased adaptive potential to their offspring