Noncommutative Common Cause Principles in Algebraic Quantum Field Theory

States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B

Entropy production of cyclic population dynamics

Entropy serves as a central observable in equilibrium thermodynamics. However, many biological and ecological systems operate far from thermal equilibrium. Here we show that entropy production can characterize the behavior of such nonequilibrium systems. To this end we calculate the entropy production for a population model that displays nonequilibrium behavior resulting from cyclic competition. At a critical point the dynamics exhibits a transition from large, limit-cycle like oscillations to small, erratic oscillations. We show that the entropy production peaks very close to the critical point and tends to zero upon deviating from it. We further provide analytical methods for computing the entropy production which agree excellently with numerical simulations.Comment: 4 pages, 3 figures and Supplementary Material. To appear in Phys. Rev. Lett.

Simultaneity as an Invariant Equivalence Relation

This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of group-invariant equivalence relations. A full examination of Newton, Galilei and Poincar\'e invariant equivalence relations in $\R^4$ is presented, which provides alternative proofs, additions and occasionally corrections of results in the literature, including Malament's theorem and some of its variants. It is argued that the interpretation of simultaneity as an invariant equivalence relation, although interesting for its own sake, does not cut in the debate concerning the conventionality of simultaneity in special relativity.Comment: Some corrections, mostly of misprints. Keywords: special relativity, simultaneity, invariant equivalence relations, Malament's theore

Three-fold way to extinction in populations of cyclically competing species

Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic population model where three species exhibit cyclic competition. The cyclic dynamics reflects the non-equilibrium nature of the species interactions. While previous work focusses on the coarsening process as a mechanism that drives the system to extinction, we found that unexpectedly the dynamics to extinction is much richer. We observed three different types of dynamics. In addition to coarsening, in the evolutionary relevant limit of large times, oscillating traveling waves and heteroclinic orbits play a dominant role. The weight of the different processes depends on the degree of mixing and the system size. By analytical arguments and extensive numerical simulations we provide the full characteristics of scenarios leading to extinction in one of the most surprising models of ecology

Traffic jams induced by rare switching events in two-lane transport

We investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular traffic. Introducing a coupling between the internal states by allowing particles to switch from one to another induces an intriguing polarization phenomenon. In a mesoscopic scaling, a rich stationary regime for the density profiles is discovered, with localized domain walls in the density profile of one of the internal states being feasible. We derive the shape of the density profiles as well as resulting phase diagrams analytically by a mean-field approximation and a continuum limit. Continuous as well as discontinuous lines of phase transition emerge, their intersections induce multi-critical behaviour

Comparison of the Effects of Early Pregnancy with Human Interferon, Alpha 2 (IFNA2), on Gene Expression in Bovine Endometrium

Interferon tau (IFNT), a type I IFN similar to alpha IFNs (IFNA), is the pregnancy recognition signal produced by the ruminant conceptus. To elucidate specific effects of bovine IFNT and of other conceptus-derived factors, endometrial gene expression changes during early pregnancy were compared to gene expression changes after intrauterine application of human IFNA2. In experiment 1, endometrial tissue samples were obtained on Day (D) 12, D15, and D18 postmating from nonpregnant or pregnant heifers. In experiment 2, heifers were treated from D14 to D16 of the estrous cycle with an intrauterine device releasing IFNA2 or, as controls, placebo lipid extrudates or PBS only. Endometrial biopsies were performed after flushing the uterus. All samples from both experiments were analyzed with an Affymetrix Bovine Genome Array. Experiment 1 revealed differential gene expression between pregnant and nonpregnant endometria on D15 and D18. In experiment 2, IFNA2 treatment resulted in differential gene expression in the bovine endometrium. Comparison of the data sets from both studies identified genes that were differentially expressed in response to IFNA2 but not in response to pregnancy on D15 or D18. In addition, genes were found that were differentially expressed during pregnancy but not after IFNA2 treatment. In experiment 3, spatiotemporal alterations in expression of selected genes were determined in uteri from nonpregnant and early pregnant heifers using in situ hybridization. The overall findings of this study suggest differential effects of bovine IFNT compared to human IFNA2 and that some pregnancy-specific changes in the endometrium are elicited by conceptus-derived factors other than IFNT

Non-Abelian Bosonization and Haldane's Conjecture

We study the long wavelength limit of a spin S Heisenberg antiferromagnetic chain. The fermionic Lagrangian obtained corresponds to a perturbed level 2S SU(2) Wess-Zumino-Witten model. This effective theory is then mapped into a compact U(1) boson interacting with Z_{2S} parafermions. The analysis of this effective theory allows us to show that when S is an integer there is a mass gap to all excitations, whereas this gap vanishes in the half-odd-integer spin case. This gives a field theory treatment of the so-called Haldane's conjecture for arbitrary values of the spin S

Common Causes and The Direction of Causation

Is the common cause principle merely one of a set of useful heuristics for discovering causal relations, or is it rather a piece of heavy duty metaphysics, capable of grounding the direction of causation itself? Since the principle was introduced in Reichenbach’s groundbreaking work The Direction of Time (1956), there have been a series of attempts to pursue the latter program—to take the probabilistic relationships constitutive of the principle of the common cause and use them to ground the direction of causation. These attempts have not all explicitly appealed to the principle as originally formulated; it has also appeared in the guise of independence conditions, counterfactual overdetermination, and, in the causal modelling literature, as the causal markov condition. In this paper, I identify a set of difficulties for grounding the asymmetry of causation on the principle and its descendents. The first difficulty, concerning what I call the vertical placement of causation, consists of a tension between considerations that drive towards the macroscopic scale, and considerations that drive towards the microscopic scale—the worry is that these considerations cannot both be comfortably accommodated. The second difficulty consists of a novel potential counterexample to the principle based on the familiar Einstein Podolsky Rosen (EPR) cases in quantum mechanics

Constraints, gauge symmetries, and noncommutative gravity in two dimensions

After an introduction into the subject we show how one constructs a canonical formalism in space-time noncommutative theories which allows to define the notion of first-class constraints and to analyse gauge symmetries. We use this formalism to perform a noncommutative deformation of two-dimensional string gravity (also known as Witten black hole).Comment: Based on lectures given at IFSAP-2004 (St.Petersburg), to be submitted to Theor. Math. Phys., dedicated to Yu.V.Novozhilov on the occasion of his 80th birthda

Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model

Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf 428}, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely the `rock-paper-scissors' or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a \emph{finite number of agents} drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems.Comment: 12 pages, 9 figures, minor correction