Ensemble averaged entanglement of two-particle states in Fock space

Recent results, extending the Schmidt decomposition theorem to wavefunctions of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and to a pair of bosons in the the Bose-Hubbard model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasised.Comment: 19 pages Latex, changed title, references added in the conclusion

Основні етапи та особливості правового регулювання фінансування будівництва залізниць на території України в другій половині ХІХ – на початку ХХ ст.

Досліджуються питання розвитку та вдосконалення залізничного транспорту України, який постає у державі як одна з ланок поліпшення соціально-економічного життя суспільства. Розкриваються проблеми нормативно-правового регулювання виникнення залізничного транспорту в Україні.Рассматриваются вопросы развития и усовершенствования железнодорожного транспорта Украины, который является для государства звеном улучшения социально-экономической жизни общества. Раскрываются проблемы нормативно-правового регулирования возникновения железнодорожного транспорта в Украине.The guestions of development and improvement of the Ukrainian railvay transport which is consideret to be as one of the directions of making better social-economic life of society are investigated. The problems of normative\loyal regulating of the appearing of railwaj transport in Ukraine (the second half of the nineteenth century)

The self-consistent gravitational self-force

I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed; I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long timescales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.Comment: 44 pages, 4 figure

Fluctuations and correlations in an individual-based model of biological coevolution

We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in previous investigations. The stationary states of the mutationless model are generally well approximated by Gaussian distributions, so that the fluctuations and correlations of the populations can be computed analytically. Several specific cases are studied by Monte Carlo simulations, and there is excellent agreement between the data and the theoretical predictions.Comment: 25 pages, 2 figure

Effects of early-life conditions on innate immune function in adult zebra finches

Early life conditions can affect individuals for life, with harsh developmental conditions resulting in lower fitness, but the underlying mechanisms are not well understood. We hypothesized that immune function may be part of the underlying mechanism, when harsh developmental conditions result in less effective immune function. We tested this hypothesis by comparing innate immune function between zebra finches (Taeniopygia guttata) in adulthood (n=230; age 108–749 days) that were reared in either small or large broods. We used this experimental background to follow up our earlier finding that finches reared in large broods have a shorter lifespan. To render a broad overview of innate immune function, we used an array of six measures: bacterial killing capacity, hemagglutination, hemolysis, haptoglobin, nitric oxide and ovotransferrin. We found no convincing evidence for effects of natal brood size on any of the six measures of innate immune function. This raised the question whether the origin of variation in immune function was genetic, and we therefore estimated heritabilities using animal models. However, we found heritability estimates to be low (range 0.04–0.11) for all measured immune variables, suggesting variation in innate immune function can largely be attributed to environmental effects independent of early-life conditions as modified by natal brood size

Effects of manipulated food availability and seasonality on innate immune function in a passerine

The innate immune system is essential for survival, yet many immune traits are highly variable between and within individuals. In recent years, attention has shifted to the role of environmental factors in modulating this variation. A key environmental factor is food availability, which plays a major role in shaping life histories, and may affect resource allocation to immune function through its effect on nutritional state. We developed a technique to permanently increase foraging costs in seed-eating birds, and leveraged this technique to study the effects of food availability on the innate immune system over a 3-year period in 230 zebra finches housed in outdoor aviaries. The immune components we studied were haptoglobin, ovotransferrin, nitric oxide, natural antibodies through agglutination, complement-mediated lysis, and killing capacity of Escherichia coli and Candida albicans, covering a broad spectrum of the innate immune system. We explored the effects of food availability in conjunction with other potentially important variables: season, age, sex and manipulated natal brood size. Increased foraging costs affected multiple components of the immune system, albeit in a variable way. Nitric oxide and agglutination levels were lower under harsh foraging conditions, while Escherichia coli killing capacity was increased. Agglutination levels also varied seasonally, but only at low foraging costs. C. albicans killing capacity was lower in winter, and even more so for animals in harsh foraging conditions that were raised in large broods. Effects of food availability on ovotransferrin were also seasonal, and only apparent in males. Haptoglobin levels were independent of foraging costs and season. Males had higher levels of immune function than females for three of the measured immune traits. Innate immune function was independent of age and manipulated natal brood size. Our finding that food availability affects innate immune function suggests that fitness effects of food availability may at least partially be mediated by effects on the immune system. However, food availability effects on innate immunity varied in direction between traits, illustrating the complexity of the immune system and precluding conclusions on the level of disease resistance

Strong Coupling Theory of Two Level Atoms in Periodic Fields

We present a new convergent strong coupling expansion for two-level atoms in external periodic fields, free of secular terms. As a first application, we show that the coherent destruction of tunnelling is a third-order effect. We also present an exact treatment of the high-frequency region, and compare it with the theory of averaging. The qualitative frequency spectrum of the transition probability amplitude contains an effective Rabi frequency.Comment: 4 pages with 3 figure