Generic Circumstances Research Articles

Multi-species thermalization cascade of energetic particles in the early universe

Heavy long-lived particles are abundant in BSM physics and will, under generic circumstances, get to dominate the energy density of the universe. The resulting matter dominated era has to end through the decay of the heavy matter component particles of mass M, and before the universe cools down to a temperature of a few MeV, in order not to upset the successful predictions of Big Bang Nucleosynthesis. The process of thermalization of their decay products, of initial energy ∼ M/2, into a thermal bath of temperature T primarily involves near-collinear splittings of energetic particles into two particles with lower energy. The correct treatment of these processes requires the inclusion of coherence effects which suppress the splitting rate. We write down and numerically solve the resulting coupled Boltzmann equations including all gauge bosons and fermions of the unbroken phase of the Standard Model (SM). We then comment on the dependence of the nonthermal spectra on the ratio M/T, as well as on the matter decay rate and branching ratios into various SM particles.

Analytic structure of three-point functions from contour deformations

We explore the analytic structure of three-point functions using contour deformations. This method allows continuing calculations analytically from the spacelike to the timelike regime. We first elucidate the case of two-point functions with explicit explanations how to deform the integration contour and the cuts in the integrand to obtain the known cut structure of the integral. This is then applied to one-loop three-point integrals. We explicate individual conditions of the corresponding Landau analysis in terms of contour deformations. In particular, the emergence and position of singular points in the complex integration plane are relevant to determine the physical thresholds. As an exploratory demonstration of this method's numerical implementation we apply it to a coupled system of functional equations for the propagator and the three-point vertex of $\phi^3$ theory. We demonstrate that under generic circumstances the three-point vertex function displays cuts which can be determined from modified Landau conditions.

Signatures of supermassive black hole binaries on maser systems

ABSTRACT We illustrate a novel signature of black hole binaries from their effect on the kinematics of water maser emission in their environments. With the help of simulations, we establish the condition for clumps to mase based on their coherence lengths calibrated to those of the known maser galaxy NGC 4258. This is then used to identify masing clumps around a binary black hole system, and quantify the kinematic and spectral differences relative to the single black hole case. For some generic circumstances, blueshifted masers around a binary black hole are found to preferentially follow the Keplerian rotation curve observed in the single black hole case. The redshifted ones, however, are found to visibly deviate from this relation, and also display more scatter with a tendency towards lower absolute values of the velocity along the line of sight. The spectrum of the masers as a function of line-of-sight velocity also shows a double peaked structure, reminiscent of recent observations of systems such as Mrk 1. Our results motivate future prospects for identifying binary black hole candidates with the help of water maser emissions.

La jurisdicción ordinaria y la indeterminación restrictiva que representa el tipo penal de prevaricato en Colombia

La indeterminación sobre la rigidez o flexibilidad de nuestro sistema de precedentes ha causado conceptualizaciones dispersas en cuanto a la obligatoriedad y alcance del derecho jurisprudencial en Colombia; la contradicción entre las facultades constitucionales de apartamiento, adición o modificación del precedente y la descripción típica del prevaricato es una de las aristas problemicas que se perfila como obstáculo del emblemático “derecho viviente” tan constitucionalmente pregonado alguna vez y tan pobremente desarrollado desde la jurisdicción ordinaria al día de hoy. La fórmula que se plantea frente al anterior problema pretende evitar que nuestros jueces de la república se auto restrinjan en el uso de sus facultades para la creación de sub reglas por temor de prevaricar. De esta forma, para abordar el asunto de la verificabilidad del criterio hermenéutico que soporta la creación de nuevas sub reglas, se encontrará en el estudio del delito de Prevaricato el necesario punto de partida que delimita los obstáculos propios de la pugna por el principio de seguridad jurídica y la confianza legítima contra la libertad en la práctica judicial interpretativa, formulando problemas como la desconfianza hacia los argumentos justificativos de los jueces o la confusa idea de control de legalidad sobre los criterios racionales del juez cuando se aparta, adiciona o modifica el carácter de ley para crear una nueva sub regla de derecho.

How likely are constituent quanta to initiate inflation?

We propose an intuitive framework for studying the problem of initial conditions in slow-roll inflation. In particular, we consider a universe at high, but sub-Planckian energy density and analyze the circumstances under which it is plausible for it to become dominated by inflated patches at late times, without appealing to the idea of self-reproduction. Our approach is based on defining a prior probability distribution for the constituent quanta of the pre-inflationary universe. To test the idea that inflation can begin under very generic circumstances, we make specific – yet quite general and well grounded – assumptions on the prior distribution. As a result, we are led to the conclusion that the probability for a given region to ignite inflation at sub-Planckian densities is extremely small. Furthermore, if one chooses to use the enormous volume factor that inflation yields as an appropriate measure, we find that the regions of the universe which started inflating at densities below the self-reproductive threshold nevertheless occupy a negligible physical volume in the present universe as compared to those domains that have never inflated.

No time for quality

Purpose – This investigation focusses on the mechanisms that obstruct an organization’s ability to develop. The purpose of this paper is to focus on short-term phenomena, which occurs during an organization’s general development process. Design/methodology/approach – The key resources in the development process include time and knowledge availability. The amount of the resources is one of basic factors of development effectiveness. From the “problems cleaner” equation, it follows that effectiveness depends on time, within which tasks are to be completed. Findings – There are a set of generic circumstances that produce specific organizational behaviors, referred to as the “culture of hurrying.” These circumstances are based on the natural expectation that organizational function is recovered as soon as possible after a failure occurs. The pathology begins when hurrying becomes a basic way to compensate for the effects of the failure, without eliminating its mechanisms. The culture of hurrying affects the organization’s ability to develop. Consequently, the conditions that stimulate the “culture of hurrying” to grow are formulated. Originality/value – Organizations managed by objectives provide examples of the culture of hurrying. On the other hand, organizations that adopt lean management illustrate how to escape from the culture of hurrying. This investigation shows that attitudes in favor of the culture of hurrying are related to the organization’s strategy.

CHALLENGES IN FORMING THE SOLAR SYSTEM'S GIANT PLANET CORES VIA PEBBLE ACCRETION

Though ~10 Earth mass rocky/icy cores are commonly held as a prerequisite for the formation of gas giants, theoretical models still struggle to explain how these embryos can form within the lifetimes of gaseous circumstellar disks. In recent years, aerodynamic-aided accretion of "pebbles," objects ranging from centimeters to meters in size, has been suggested as a potential solution to this long-standing problem. While pebble accretion has been demonstrated to be extremely effective in local simulations that look at the detailed behavior of these pebbles in the vicinity of a single planetary embryo, to date there have been no global simulations demonstrating the effectiveness of pebble accretion in a more complicated, multi-planet environment. Therefore, we have incorporated the aerodynamic-aided accretion physics into LIPAD, a Lagrangian code that can follow the collisional / accretional / dynamical evolution of a protoplanetary system, to investigate how pebble accretion manifests itself in the larger planet formation picture. We find that under generic circumstances, pebble accretion naturally leads to an "oligarchic" type of growth in which a large number of planetesimals grow to similar-sized planets. In particular, our simulations tend to form hundreds of Mars- and Earth-mass objects between 4 and 10 AU. While the merging of some oligarchs may allow them to grow massive enough to form giant planet cores, leftover oligarchs lead to planetary systems that cannot be consistent with our own solar system. We investigate various ideas presented in the literature (including evaporation fronts and planet traps) and find that none easily overcome this tendency toward oligarchic growth.

Sustainable entanglement production from a quantum field

We propose a protocol by which entanglement can be extracted repeatedly from a quantum field. In analogy with prior work on entanglement harvesting, we call this protocol entanglement farming. It consists of successively sending pairs of unentangled particles through an optical cavity. Using non-perturbative Gaussian methods, we show that in certain generic circumstances this protocol drives the cavity field towards a non-thermal metastable state. This state of the cavity is such that successive pairs of unentangled particles sent through the cavity will reliably emerge significantly entangled. We calculate thermodynamic aspects of the harvesting process, such as energies and entropies, and also the long-term behavior beyond the few-mode approximation. Significant for possible experimental realizations is the fact that this entangling fixed point state of the cavity is reached largely independently of the initial state in which the cavity was prepared. Our results suggest that reliable entanglement farming on the basis of such a fixed point state should be possible also in various other experimental settings, namely with the to-be-entangled particles replaced by arbitrary qudits and with the cavity replaced by a suitable reservoir system.

Yang–Mills condensate dark energy coupled with matter and radiation

The coincidence problem is studied for the dark energy model of effective Yang–Mills condensate (YMC) in a flat expanding universe during the matter-dominated stage. The YMC energy ρy(t) is taken to represent the dark energy, which is coupled either with the matter ρm(t), or with both the matter and the radiation components ρr(t). The effective YM Lagrangian is completely determined by the quantum field theory up to 1-loop order with an energy scale ∼10−3 eV as a model parameter, and for each coupling, there is an extra model parameter. We have studied extensively the coupling models: the YMC decaying into the matter and the radiation; or vice versa the matter and radiation decaying into the YMC. It is found that, starting from the equality of radiation-matter ρmi = ρri, for a wide range of initial conditions of ρyi = (10−10, 10−2)ρmi, the models have a scaling solution during the early stages, and the YMC levels off and becomes dominant at late time, and the present state with Ωy ≃ 0.7, Ωm ≃ 0.3 and Ωr ≃ 10−5 is always achieved. If the YMC decays into a component, then this component also levels off later and approaches a constant value asymptotically, and the equation of state (EoS) of the YMC wy = ρy/py crosses over −1 and takes the value wy ≃ −1.1 at z = 0. If the matter and radiation decay into the YMC, then ρm(t) ∝ a(t)−3 and ρr(t) ∝ a(t)−4 approximately for all the time, and wy approaches −1 but does not cross over −1. We have also demonstrated that, at t → ∞, the coupled dynamics for (ρy(t), ρm(t), ρr(t)) is a stable attractor. Therefore, under generic circumstances, the existence of the scaling solution during the early stages and the subsequential exit from the scaling regime around z ≃ (0.3–0.5) are inevitable. Thus the coincidence problem can be naturally solved in the YMC dark energy models.

The circumstances of justice

In this article, I analyze the circumstances of justice, that is, the background conditions that are necessary and sufficient for justice to exist between individual parties in society. Contemporary political philosophers almost unanimously accept an account of these circumstances attributed to David Hume. I argue that the conditions of this standard account are neither sufficient nor necessary conditions for justice. In particular, I contend that both a Hobbesian state of nature and a prisoner’s dilemma are cases in which the conditions of the standard account obtain and yet no justice exists between parties. I propose an alternative set of generic circumstances of justice motivated by examples from game theory. Parties are in these generic circumstances with respect to each other when: (1) they are engaged in a conflictual coordination game with multiple strict Nash equilibrium points where, at any of these equilibria, some parties do not receive their greatest payoffs, and (2) they have common knowledge that each party is rational and follows her end of a strict equilibrium where no party receives her greatest payoff. These two conditions reflect the idea that justice requires all parties to make some sacrifices so that others can have more of the goods they need and want. I argue that these generic circumstances are necessary and sufficient conditions for parties to follow generic norms of justice, that is, mutually beneficial practices that require some sacrifices.

On the number of solutions for the two-point boundary value problem on Riemannian manifolds

We study the solutions joining two fixed points of a time-independent dynamical system on a Riemannian manifold ( M, g) from an enumerative point of view. We prove a finiteness result for solutions joining two points p, q∈ M that are non-conjugate in a suitable sense, under the assumption that ( M, g) admits a non-trivial convex function. We discuss in some detail the notion of conjugacy induced by a general dynamical system on a Riemannian manifold. Using techniques of infinite dimensional Morse theory on Hilbert manifolds we also prove that, under generic circumstances, the number of solutions joining two fixed points is odd. We present some examples where our theory applies.

Weyling the time away: the non-unitary implementability of quantum field dynamics on curved spacetime

The simplest case of quantum field theory on curved spacetime—that of the Klein–Gordon field on a globally hyperbolic spacetime—reveals a dilemma: In generic circumstances, either there is no dynamics for this quantum field, or else there is a dynamics that is not unitarily implementable. We do not try to resolve the dilemma here, but endeavour to spell out the consequences of seizing one or the other horn of the dilemma.

The Morse index theorem in semi-Riemannian geometry

We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two submanifolds. The key role of the theory is played by the notion of the Maslov index of a semi-Riemannian geodesic, which is a homological invariant and it substitutes the notion of geometric index in Riemannian geometry. Under generic circumstances, the Maslov index of a geodesic is computed as a sort of algebraic count of the conjugate points along the geodesic. For nonpositive definite metrics the index of the index form is always infinite; in this paper we prove that the space of all variations of a given geodesic has a natural splitting into two infinite dimensional subspaces, and the Maslov index is given by the difference of the index and the coindex of the restriction of the index form to these subspaces. In the case of variable endpoints, two suitable correction terms, defined in terms of the endmanifolds, are added to the equality. Using appropriate change of variables, the theory is entirely extended to the more general case of symplectic differential systems, that can be obtained as linearizations of the Hamilton equations. The main results proven in this paper were announced in Piccione and Tausk (C. R. Acad. Sci. Paris 331 (5) (2000) 385).

An Index Theorem for Non-Periodic Solutions of Hamiltonian Systems

We consider a Hamiltonian setup(M, ω, H, L, ,P), where (M, ω) is a symplectic manifold, L is a distribution of Lagrangian subspaces in M, P a Lagrangian submanifold of M, H is a smooth time dependent Hamiltonian function on M and : ( a, b) ! M is an integral curve of the Hamiltonian flow ~ H starting at P. We do not require any convexity property of the Hamiltonian function H. Under the assump- tion that ( b) is not P-focal it is introduced the Maslov index imaslov() of given in terms of the first relative homology group of the Lagrangian G rassmannian; under generic circumstances imaslov() is computed as a sort of algebraic count of the P-focal points along . We prove the following version of the Index Theorem: under suitable hypothe- ses, the Morse index of the Lagrangian action functional restricted to suitable variations of is equal to the sum of imaslov() and a convexity term of the Hamiltonian H rela- tive to the submanifold P. When the result is applied to the case of the cotangent bundle M = T Mof a semi-Riemannian manifold (M, g) and to the geodesic Hamiltonian H(q, p) = 1 g 1 (p, p), we obtain a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics with variable endpoints in Riemannian geometry.

A generalized index theorem for Morse–Sturm systems and applications to semi-Riemannian geometry

We prove an extension of the Index Theorem for Morse–Sturm systems of the form −V ′′ + RV = 0, where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus the corresponding differential operator is not self-adjoint. The result is then applied to the case of a Jacobi equation along a geodesic in a Lorentzian manifold, obtaining an extension of the Morse Index Theorem for Lorentzian geodesics with variable initial endpoints. Given a Lorentzian manifold (M, g), we consider a geodesic γ in M starting orthogonally to a smooth submanifold P of M. Under suitable hypotheses, satisfied, for instance, if (M, g) is stationary, the theorem gives an equality between the index of the second variation of the action functional f at γ and the sum of the Maslov index of γ with the index of the metric g on P . Under generic circumstances, the Maslov index of γ is given by an algebraic count of the P-focal points along γ. Using the Maslov index, we obtain the global Morse relations for geodesics between two fixed points in a stationary Lorentzian manifold.

Electron scattering through a quantum dot: A phase lapse mechanism

The scattering phase shift of an electron transferred through a quantum dot is studied within a model Hamiltonian, accounting for both the electron--electron interaction in the dot and a finite temperature. It is shown that, unlike in an independent electron picture, this phase may exhibit a phase lapse of $ \pi $ {\em between } consecutive resonances under generic circumstances.