Unstable Resonances Research Articles

Structure of near-threshold resonances with new interpretation scheme of complex compositeness

The nature of near-threshold resonances is quantitatively studied with a new interpretation scheme using the complex compositeness. A difficulty was known in the understanding of the internal structure of unstable resonances because their complex compositeness is not an interpretable measure. To overcome this problem, we develop a new interpretation scheme respecting the ambiguous aspects of the identification of the internal structure of resonances. We then apply the interpretation scheme to the near-threshold resonances slightly above the threshold, described by the effective range expansion. With the new interpretation scheme, we show that near-threshold resonances are dominated by the non-molecular component. Namely, even in the near-threshold region, the nature of resonances is sharply contrasted with bound states whose internal structure is usually molecular dominant.

Matrix element corrections in the Pythia8 parton shower in the context of matched simulations at next-to-leading order

We discuss the role of matrix element corrections (MEC) to parton showers in the context of MC@NLO-type matchings for processes that feature unstable resonances, where MEC are liable to result in double-counting issues, and are thus generally not employed. By working with Pythia8, we show that disabling all MEC is actually unnecessary in computations based on the narrow-width approximation, and we propose alternative MEC settings which, while still avoiding double counting, allow one to include hard-recoil effects in the simulations of resonance decays. We illustrate our findings by considering tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\bar{t}$$\\end{document} production at the LHC, and by comparing MadGraph5-aMC@NLO predictions with those of POWHEG-BOX and standalone Pythia8.

Propagators and widths of physical and purely virtual particles in a finite interval of time

We study the free and dressed propagators of physical and purely virtual particles in a finite interval of time τ and on a compact space manifold Ω, using coherent states. In the free-field limit, the propagators are described by the entire function (ez– 1 – z)/z2, whose shape on the real axis is similar to the one of a Breit-Wigner function, with an effective width around 1/τ. The real part is positive, in agreement with unitarity, and remains so after including the radiative corrections, which shift the function into the physical half plane. We investigate the effects of the restriction to finite τ on the problem of unstable particles vs resonances, and show that the muon observation emerges from the right physical process, differently from what happens at τ = ∞. We also study the case of purely virtual particles, and show that, if τ is small enough, there exists a situation where the geometric series of the self-energies is always convergent. The plots of the dressed propagators show testable differences: while physical particles are characterized by the usual, single peak, purely virtual particles are characterized by twin peaks.

Modifying the Dyson series for unstable particles and resonances

In this work, we introduce a modification of the Dyson series based on the perturbative unitarity as a starting point. The presented approach systematically avoids singularities and double-counting related to the presence of unstable particles as intermediate states and, at the same time, it does not rely on a specific choice of the renormalization scheme.

Влияние эффекта Ярковского на орбитальные резонансы астероидов с малыми перигелийными расстояниями

The paper presents the study results of the Yarkovsky effect influence on the resonant characteristics of asteroids with small perihelion distances. Out of 52 studied objects, 27 asteroids were identified that move in the vicinity of stable and unstable low-order mean motion resonances with major planets. The evolution of the asteroids orbits is constructed with and without the Yarkovsky effect, and the behavior of the resonance characteristics in both cases is analyzed. The effect was taken into account by including the perturbation from the transversal acceleration A2, the values of which for the presented objects were obtained earlier by the authors of this work. It is shown that the Yarkovsky effect influence on stable resonances is insignificant and leads to small changes in the libration amplitude of the resonance characteristics. The stability of the resonance is preserved. With unstable resonant interaction, the number of passages through the exact commensurability changes, and for some asteroids the resonance becomes more stable.

Long term orbital dynamics of a retrograde Centaur 2006 RJ2

Centaurs are small bodies whose semi-major axes are located between Jupiter and Neptune. They have chaotic orbits and may be in orbital resonances with giant planets. An orbital resonance occurs when a simple commensurability presents between some fundamental frequencies of orbital elements. One of the resonance states is 1:1 (mean motion) resonance or co-orbital with the respected planet. This resonance can also occur in high inclination Centaurs. This study describes the results of long term orbital integration of a retrograde Centaur 2006 RJ2 (inclination of 165°) for 200,000 years. Resonance state of 2006 RJ2 was examined using the FAIR (Fast Identification of Mean Motion Resonance) method for 243 orbital clones with automation by developing Python codes. We report that 2006 RJ2 may be in retrograde 1:1 resonance with Saturn for about 160,000 years in the future. However, the clones exhibit chaotic orbits and show many temporally unstable resonances. Since the quality of its orbital elements is not quite precise, 2006 RJ2 shows a low possibility in the state of long retrograde 1:1 resonance with Saturn.

Analysis of the dynamical evolution of the Quadrantid meteoroid stream

We investigate numerically the dynamical evolution of simulated meteoroid stream of the Quadrantids ejected from the parent body of the asteroid (196256) 2003 EH1. The main goal of this work is to identify mean motion and secular resonances and to study the mutual influence of resonance relations and close encounters with the major planets. Since the dynamics of this asteroid is predictable only on short time intervals, and not only close and/or multiple close encounters with major planets, but also the presence of at least one unstable resonance can lead to chaotic motion of test particles, we studied their resonant dynamics. The dynamical evolution of the test particles expects possible scenario for resonant motion. We conjecture that the reasons of chaos are the overlap of stable secular resonances and unstable mean motions resonances and close and/or multiple close encounters with the major planets. The estimate of the stability of orbits in which the particles in simulations moved was carried out by analyzing the behavior of the parameter MEGNO (Mean Exponential Growth factor of Nearby Orbits). The larger part of the identified resonances is stable. We found a peculiar behavior for this stream. Here, we show that the orbits of some ejected particles are strongly affected by the Lidov–Kozai mechanism that protects them from close encounters with Jupiter. Lack of close encounters with Jupiter leads to a rather smooth growth in the parameter MEGNO and the behavior imply the stable motion of simulation particles of the Quadrantids meteoroid stream.

The KdV approximation for a system with unstable resonances

The KdV equation can be derived via multiple scaling analysis for the approximate description of long waves in dispersive systems with a conservation law. In this paper, we justify this approximation for a system with unstable resonances by proving estimates between the KdV approximation and true solutions of the original system. By working in spaces of analytic functions, the approach will allow us to handle more complicated systems without a detailed discussion of the resonances and without finding a suitableenergy.

Incorrect Estimates by the Four Wave Interaction(FWI) system for the Fermi‐Pasta‐Ulam(FPU) System

AbstractRecently it was proved in [9] that the nonlinear Schrödinger equation fails to predict accurately the dynamics of an original system because of unstable resonances. By extending the ideas in [9], we prove a similar result for the Four Wave Interaction System.

Superradiant instability of charged scalar fields in higher-dimensional Reissner-Nordström-de Sitter black holes

Black holes possess trapping regions which lead to intriguing dynamical effects. By properly scattering test fields off a black hole, one can extract energy from it, leading to the growth of the amplitude of the test field in expense of the black hole's energy. Such a dynamical phenomenon is called superradiance. Here, we study charged-scalar-field instabilities of Reissner-Nordstr\"{o}m black holes immersed in a $d-$dimensional de Sitter Universe. By performing a thorough frequency-domain analysis we compute the unstable quasinormal resonances and link their presence with a novel family of quasinormal modes associated with the existence and timescale of the cosmological horizon of pure de Sitter spacetime. Our results indicate that such an instability is caused by superradiance, while the increment of dimensions amplifies the growth rate and enlarges the region of the parameter space where, both massless and massive, test fields are unstable.

Compositeness of hadron resonances in finite volume

We develop a theoretical framework to quantify the structure of unstable hadron resonances. With the help of the corresponding system in a finite volume, we define the compositeness of resonance states which can be interpreted as a probability. This framework is used to study the structure of the scalar mesons f_0(980) and a_0(980). In both mesons, the Kbar K component dominates about a half of the wave function. The method is also applied to the Lambda(1405) resonance. We argue that a single energy level in finite volume represents the two eigenstates in infinite volume. The KbarK N component of Lambda(1405), including contributions from both eigenstates, is found to be 58%, and the rest is composed of the pi Sigma and other channels.

Crisis of the chaotic attractor of a climate model: a transfer operator approach

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are known to be characterised by a single or a pair of characteristic exponents crossing the imaginary axis. As a result, the approach of such bifurcations in the presence of noise can be inferred from the slowing down of the decay of correlations (Held and Kleinen 2004 Geophys. Res. Lett. 31 1–4). On the other hand, little is known about global bifurcations involving high-dimensional attractors with several positive Lyapunov exponents.It is known that the global stability of chaotic attractors may be characterised by the spectral properties of the Koopman (Mauroy and Mezić 2016 IEEE Trans. Autom. Control 61 3356–69) or the transfer operators governing the evolution of statistical ensembles. Accordingly, it has recently been shown (Tantet 2017 J. Stat. Phys. 1–33) that a boundary crisis in the Lorenz flow coincides with the approach to the unit circle of the eigenvalues of these operators associated with motions about the attractor, the stable resonances. A second class of resonances, the unstable resonances, are responsible for the decay of correlations and mixing on the attractor. In the deterministic case, these cannot be expected to be affected by general boundary crises.Here, however, we give an example of a chaotic system in which slowing down of the decay of correlations of some observables does occur at the approach of a boundary crisis. The system considered is a high-dimensional, chaotic climate model of physical relevance. Moreover, coarse-grained approximations of the transfer operators on a reduced space, constructed from a long time series of the system, give evidence that this behaviour is due to the approach of unstable resonances to the unit circle. That the unstable resonances are affected by the crisis can be physically understood from the fact that the process responsible for the instability, the ice-albedo feedback, is also active on the attractor. Finally, we discuss implications regarding response theory and the design of early-warning signals.

Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle-Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the phase space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not ag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises.

Analytic treatment of the excited instability spectra of the magnetically charged SU(2) Reissner-Nordstr\xf6m black holes

The magnetically charged SU(2) Reissner-Nordström black-hole solutions of the coupled nonlinear Einstein-Yang-Mills field equations are known to be characterized by infinite spectra of unstable (imaginary) resonances {ωn(r+, r−)}n = 0n = ∞ (here r± are the black-hole horizon radii). Based on direct numerical computations of the black-hole instability spectra, it has recently been observed that the excited instability eigenvalues of the magnetically charged black holes exhibit a simple universal behavior. In particular, it was shown that the numerically computed instability eigenvalues of the magnetically charged black holes are characterized by the small frequency universal relation ωn(r+ − r−) = λn, where {λn} are dimensionless constants which are independent of the black-hole parameters. In the present paper we study analytically the instability spectra of the magnetically charged SU(2) Reissner-Nordström black holes. In particular, we provide a rigorous analytical proof for the numerically-suggested universal behavior ωn(r+ − r−) = λn in the small frequency ωnr+ ≪ (r+ − r−)/r+ regime. Interestingly, it is shown that the excited black-√hole resonances are characterized by the simple universal relation ωn + 1/ωn = e− 2π/3. Finally, we confirm our analytical results for the black-hole instability spectra with numerical computations.

Radial vibrations of BPS skyrmions

We study radial vibrations of spherically symmetric skyrmions in the BPS Skyrme model. Concretely, we numerically solve the linearised field equations for small fluctuations in a skyrmion background, both for linearly stable oscillations and for (unstable) resonances. This is complemented by numerical solutions of the full nonlinear system, which confirm all the results of the linear analysis. In all cases, the resulting fundamental excitation provides a rather accurate value for the Roper resonance, supporting the hypothesis that the BPS Skyrme model already gives a reasonable approximate description of this resonance. Further, for many potentials additional higher resonances appear, again in agreement with known experimental results.

The Impact of Pneumatic Chemistry on Robert Southey's Madoc

ABSTRACTThis essay considers the effects of Robert Southey's encounters with pneumatic chemistry on his epic Madoc. The 1797–1799 draft of the poem describes air differently from the published 1805 version, which was extensively revised in the years following Southey's experiences with nitrous oxide at the Pneumatic Institution. Matter, in general, appears particularly fraught and complex in the 1805 Madoc—specifically, an emphasized metonymic materiality there links to unstable metaphoric resonances. Examining Southey's response to nitrous oxide along with the work of pneumatic chemists and the 1805 Madoc's descriptions of material experience, this essay argues that Southey developed Madoc's formal complexities in light of new senses of materiality he arrived at with regard to pneumatic chemistry.

Importance of resonance widths in low-energy scattering of weakly bound light-mass nuclei

What effect do particle-emitting resonances have on the scattering cross section? What physical considerations are necessary when modelling these resonances? These questions are important when theoretically describing scattering experiments with radioactive ion beams which investigate the frontiers of the table of nuclides, far from stability. Herein, a novel method is developed that describes resonant nuclear scattering from which centroids and widths in the compound nucleus are obtained when one of the interacting bodies has particle unstable resonances. The method gives cross sections without unphysical behavior that is found if simple Lorentzian forms are used to describe resonant target states. The resultant cross sections differ significantly from those obtained when the states in the coupled channel calculations are taken to have zero width, and compound-system resonances are better matched to observed values.

Special Features of the Structure of Secular Resonances in the Dynamics of Near-Earth Space Objects

The special features of the structure of secular resonances in the near-earth orbital space bounded by the following range of orbital parameters: semimajor axis from 8000 to 55 000 km, inclination from 0 to 90°, and eccentricity equal to 0.01, 0.6, and 0.8 are analyzed. The influence of stable and unstable secular resonances on the long-term orbital evolution of near-earth space objects is also considered. It is demonstrated that the joint effect of the stable secular resonances of different spectral classes does not violate the regularity of motion. The chaoticity arises when stable secular resonances of one spectral class are imposed.

From photoelectron detachment spectra of BrHBr(-), BrDBr(-) and IHI(-), IDI(-) to vibrational bonding of BrMuBr and IMuI.

Photoelectron detachment XLX(-)(00(0)0) + hν → XLX(vib) + e(-) + KER (X = Br or I, L = H or D) at sufficiently low temperatures photoionizes linear dihalogen anions XLX(-) in the vibrational ground state (v1v2 (l)v3 = 00(0)0) and prepares the neutral radicals XLX(vib) in vibrational states (vib). At the same time, part of the photon energy (hν) is converted into kinetic energy release (KER) of the electron [R. B. Metz, S. E. Bradforth, and D. M. Neumark, Adv. Chem. Phys. 81, 1 (1992)]. The process may be described approximately in terms of a Franck-Condon type transfer of the vibrational wavefunction representing XLX(-)(00(0)0) from the domain close to the minimum of its potential energy surface (PES) to the domain close to the linear transition state of the PES of the neutral XLX. As a consequence, prominent peaks of the photoelectron detachment spectra (pds) correlate with the vibrational energies EXLX,vib of states XLX(vib) which are centered at linear transition state. The corresponding vibrational quantum numbers may be labeled vib = (v1v2 (l)v3) = (00(0)v3). Accordingly, the related most prominent peaks in the pds are labeled v3. We construct a model PES which mimics the "true" PES in the domain of transition state such that it supports vibrational states with energies EXLX,pds,00(0)v3 close to the peaks of the pds labeled v3 = 0, 2, and 4. Subsequently, the same model PES is also used to calculate approximate values of the energies EXMuX,00(0)0 of the isotopomers XMuX(00(0)0). For the heavy isotopomers XHX and XDX, it turns out that all energies EXLX,00(0)v3 are above the threshold for dissociation, which means that all heavy XLX(00(0)v3) with wavefunctions centered at the transition state are unstable resonances with finite lifetimes. Turning the table, bound states of the heavy XLX are van der Waals (vdW) bonded. In contrast, the energies EXMuX,00(0)0 of the light isotopomers XMuX(00(0)0) are below the threshold for dissociation, with wavefunctions centered at the transition state. This means that XMuX(00(0)0) are vibrationally bonded. This implies a fundamental change of the nature of chemical bonding, from vdW bonding of the heavy XHX, XDX to vibrational bonding of XMuX. For BrMuBr, the present results derived from experimental pds of BrHBr(-) and BrDBr(-) confirm the recent discovery of vibrational bonding based on quantum chemical ab initio calculations [D. G. Fleming, J. Manz, K. Sato, and T. Takayanagi, Angew. Chem., Int. Ed. 53, 13706 (2014)]. The extension from BrLBr to ILI means the discovery of a new example of vibrational bonding. These empirical results for the vibrational bonding of IMuI, derived from the photoelectron spectra of IHI(-) and IDI(-), are supported by ab initio simulations of the spectra and of the wavefunction representing vibrational bonding of IMuI.

Parametrically excited helicopter ground resonance dynamics with high blade asymmetries

The present work is aimed at verifying the influence of high asymmetries in the variation of in-plane lead-lag stiffness of one blade on the ground resonance phenomenon in helicopters. The periodical equations of motions are analyzed by using Floquet's Theory (FM) and the boundaries of instabilities predicted. The stability chart obtained as a function of asymmetry parameters and rotor speed reveals a complex evolution of critical zones and the existence of bifurcation points at low rotor speed values. Additionally, it is known that when treated as parametric excitations; periodic terms may cause parametric resonances in dynamic systems, some of which can become unstable. Therefore, the helicopter is later considered as a parametrically excited system and the equations are treated analytically by applying the Method of Multiple Scales (MMS). A stability analysis is used to verify the existence of unstable parametric resonances with first and second-order sets of equations. The results are compared and validated with those obtained by Floquet's Theory. Moreover, an explanation is given for the presence of unstable motion at low rotor speeds due to parametric instabilities of the second order.