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At least 1,207 records · Page 67

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DOE OSTI2014

Classical and quantum dynamics in an inverse square potential

The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence of bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Normal form decomposition for Gaussian-to-Gaussian superoperators

In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

FIRST-ORDER RESONANCE OVERLAP AND THE STABILITY OF CLOSE TWO-PLANET SYSTEMS

Motivated by the population of observed multi-planet systems with orbital period ratios 1 < P{sub 2}/P{sub 1} {approx}< 2, we study the long-term stability of packed two-planet systems. The Hamiltonian for two massive planets on nearly circular and nearly coplanar orbits near a first-order mean motion resonance can be reduced to a one-degree-of-freedom problem. Using this analytically tractable Hamiltonian, we apply the resonance overlap criterion to predict the onset of large-scale chaotic motion in close two-planet systems. The reduced Hamiltonian has only a weak dependence on the planetary mass ratio m{sub 1}/m{sub 2}, and hence the overlap criterion is independent of the planetary mass ratio at lowest order. Numerical integrations confirm that the planetary mass ratio has little effect on the structure of the chaotic phase space for close orbits in the low-eccentricity (e {approx}< 0.1) regime. We show numerically that orbits in the chaotic web produced primarily by first-order resonance overlap eventually experience large-scale erratic variation in semimajor axes and are therefore Lagrange unstable. This is also true of the orbits in this overlap region which satisfy the Hill criterion. As a result, we can use the first-order resonance overlap criterion as an effective stability criterion for pairs of observed planets. We show that for low-mass ({approx}< 10 M{sub Circled-Plus }) planetary systems with initially circular orbits the period ratio at which complete overlap occurs and widespread chaos results lies in a region of parameter space which is Hill stable. Our work indicates that a resonance overlap criterion which would apply for initially eccentric orbits likely needs to take into account second-order resonances. Finally, we address the connection found in previous work between the Hill stability criterion and numerically determined Lagrange instability boundaries in the context of resonance overlap.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Accessing the quark orbital angular momentum with Wigner distributions

The quark orbital angular momentum (OAM) has been recognized as an important piece of the proton spin puzzle. A lot of effort has been invested in trying to extract it quantitatively from the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs), which are accessed in high-energy processes and provide three-dimensional pictures of the nucleon. Recently, we have shown that it is more natural to access the quark OAM from the phase-space or Wigner distributions. We discuss the concept of Wigner distributions in the context of quantum field theory and show how they are related to the GPDs and the TMDs. We summarize the different definitions discussed in the literature for the quark OAM and show how they can in principle be extracted from the Wigner distributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Equivalence of two independent calculations of the higher order guiding center Lagrangian

The difference between the guiding center phase-space Lagrangians derived in J. W. Burby et al. [Phys. Plasmas 20, 072105 (2013)] and F. I. Parra and I. Calvo [Plasma Phys. Controlled Fusion 53, 045001 (2011)] is due to a different definition of the guiding center coordinates. In this brief communication, the difference between the guiding center coordinates is calculated explicitly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

New measurement of inclusive deep inelastic scattering cross sections at HERA

A combined measurement is presented of all inclusive deep inelastic cross sections measured by the H1 and ZEUS collaborations in neutral and charged current unpolarised e{sup ±}p scattering at HERA. The H1 and ZEUS collaborations collected total integrated luminosities of approximately 500 pb{sup −1} each, divided about equally between e{sup +}p and e{sup −}p scattering. They include data taken at electron (positron) beam energy of 27.5 GeV and proton beam energies of 920, 820, 575 and 460 GeV corresponding to centre-of-mass energy of 320, 300, 251 and 225 GeV respectively. This enabled the two collaborations to explore a large phase space in Bjorken x and negative four-momentum-transfer squared, Q{sup 2}. The combination method takes the correlations of the systematic uncertainties into account, resulting in improved accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Maps of the little bangs through energy density and temperature fluctuations

Heavy-ion collisions at ultra-relativistic energies are often referred to as little bangs. We propose for the first time to map the heavy-ion collisions at ultra-relativistic energies, similar to the maps of the cosmic microwave background radiation, using fluctuations of energy density and temperature in small phase space bins. We study the evolution of fluctuations at each stage of the collision using an event-by-event hydrodynamic framework. We demonstrate the feasibility of making fluctuation maps from experimental data and its usefulness in extracting considerable information regarding the early stages of the collision and its evolution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Hamiltonian analysis of higher derivative scalar-tensor theories

We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Hybrid Vlasov-Maxwell simulations of two-dimensional turbulence in plasmas

Turbulence in plasmas is a very challenging problem since it involves wave-particle interactions, which are responsible for phenomena such as plasma dissipation, acceleration mechanisms, heating, temperature anisotropy, and so on. In this work, a hybrid Vlasov-Maxwell numerical code is employed to study local kinetic processes in a two-dimensional turbulent regime. In the present model, ions are treated as a kinetic species, while electrons are considered as a fluid. As recently reported in [S. Servidio, Phys. Rev. Lett. 108, 045001 (2012)], nearby regions of strong magnetic activity, kinetic effects manifest through a deformation of the ion velocity distribution function that consequently departs from the equilibrium Maxwellian configuration. Here, the structure of turbulence is investigated in detail in phase space, by evaluating the high-order moments of the particle velocity distribution, i.e., temperature, skewness, and kurtosis. This analysis provides quantitative information about the non-Maxwellian character of the system dynamics. This departure from local thermodynamic equilibrium triggers several processes commonly observed in many astrophysical and laboratory plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Lyapunov Characteristics of Oscillation, Rotation, and Wandering of Solutions of Differential Systems

A number of Lyapunov exponents are defined for solutions of linear systems on the half-line. These exponents are responsible for such properties of the solutions as oscillation, rotation, and wandering and are defined in terms of certain functionals applied to the solutions on finite intervals as a result of two operations: upper or lower averaging in time and minimization over all bases in the phase space. We consider important special cases of systems: those of a low order, autonomous systems, those associated with equations of an arbitrary order. We obtain a set of relations (equalities and inequalities) between the said exponents, together with their refined values in special cases. It is shown that this set is complete in the sense that it cannot be extended or strengthened by any other meaningful relation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Structural and optical properties of MgO doped ZnO

Samples of ZnO, Zn{sub 0.5}Mg{sub 0.5}O and MgO were prepared by co-precipitation method. X-ray diffraction (XRD) pattern infers that the sample of ZnO is in single-phase wurtzite structure (hexagonal phase, space group P6{sub 3}mc), MgO crystallizes in cubic Fd3m space group and Zn{sub 0.5}Mg{sub 0.5}O represents mixed nature of ZnO and MgO lattices. Similar features were observed from Raman spectroscopy. The energy band gaps estimated from UV-Vis spectroscopy are found to be 4.21 and 3.42 eV for ZnO and Zn{sub 0.5}Mg{sub 0.5}O samples respectively.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Translation invariant time-dependent solutions to massive gravity

Homogeneous time-dependent solutions of massive gravity generalise the plane wave solutions of the linearised Fierz-Pauli equations for a massive spin-two particle, as well as the Kasner solutions of General Relativity. We show that they also allow a clear counting of the degrees of freedom and represent a simplified framework to work out the constraints, the equations of motion and the initial value formulation. We work in the vielbein formulation of massive gravity, find the phase space resulting from the constraints and show that several disconnected sectors of solutions exist some of which are unstable. The initial values determine the sector to which a solution belongs. Classically, the theory is not pathological but quantum mechanically the theory may suffer from instabilities. The latter are not due to an extra ghost-like degree of freedom.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Exotic quarkonium states in CMS

The studies of the production of the X(3872), either prompt or from B-hadron decays, and of the J/ψϕ mass spectrum in B-hadron decays have been carried out by using pp collisions at √s = 7 TeV collected with the CMS detector at the LHC. The cross-section ratio of the X(3872) with respect to the ψ(2S) in the J/ψπ{sup +}π{sup −} decay channel and the fraction of X(3872) coming from B-hadron decays are measured as a function of transverse momentum (p{sub T}), covering unprecedentedly high values of p{sub T}. For the first time, the prompt X(3872) cross section times branching fraction is extracted differentially in p{sub T} and compared with NRQCD predictions. The dipion invariant-mass spectrum of the J/ψπ{sup +}π{sup −} system in the X(3872) decay is also investigated. A peaking structure in the J/ψϕ mass spectrum near threshold is observed in B{sup ±} → J/ψϕK{sup ±} decays. The data sample, selected on the basis of the dimuon decay mode of the J/ψ, corresponds to an integrated luminosity of 5.2 fb{sup −1}. Fitting the structure to an S-wave relativistic Breit–Wigner lineshape above a three-body phase-space nonresonant component gives a signal statistical significance exceeding five standard deviations. The fitted mass and width values are m = 4148.0 ± 2.4(stat.) ± 6.3(syst.) MeV and Γ = 28+15 − 11(stat.) ± 19(syst.) MeV, respectively. Evidence for an additional peaking structure at higher J/ψϕ mass is also reported.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Electron Scattering by High-frequency Whistler Waves at Earth’s Bow Shock

Electrons are accelerated to non-thermal energies at shocks in space and astrophysical environments. While different mechanisms of electron acceleration have been proposed, it remains unclear how non-thermal electrons are produced out of the thermal plasma pool. Here, we report in situ evidence of pitch-angle scattering of non-thermal electrons by whistler waves at Earth’s bow shock. On 2015 November 4, the Magnetospheric Multiscale (MMS) mission crossed the bow shock with an Alfvén Mach number ∼11 and a shock angle ∼84°. In the ramp and overshoot regions, MMS revealed bursty enhancements of non-thermal (0.5–2 keV) electron flux, correlated with high-frequency (0.2–0.4 Ω{sub ce}, where Ω{sub ce} is the cyclotron frequency) parallel-propagating whistler waves. The electron velocity distribution (measured at 30 ms cadence) showed an enhanced gradient of phase-space density at and around the region where the electron velocity component parallel to the magnetic field matched the resonant energy inferred from the wave frequency range. The flux of 0.5 keV electrons (measured at 1 ms cadence) showed fluctuations with the same frequency. These features indicate that non-thermal electrons were pitch-angle scattered by cyclotron resonance with the high-frequency whistler waves. However, the precise role of the pitch-angle scattering by the higher-frequency whistler waves and possible nonlinear effects in the electron acceleration process remains unclear.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Communication: HK propagator uniformized along a one-dimensional manifold in weakly anharmonic systems

A simplification of the Heller-Herman-Kluk-Kay (HK) propagator is presented that does not suffer from the need for an increasing number of trajectories with dimensions of the system under study. This is accomplished by replacing HK’s uniformizing integral over all of phase space by a one-dimensional curve that is appropriately selected to lie along the fastest growing manifold of a defining trajectory. It is shown that this modification leads to eigenspectra of quantum states in weakly anharmonic systems that can outperform the comparatively computationally cheap thawed Gaussian approximation method and frequently approach the accuracy of spectra obtained with the full HK propagator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Quantum decay in renormalizable field theories: Quasiparticle formation, Zeno and anti-Zeno effects

In a renormalizable theory the survival probability of an unstable quantum state features divergences as a consequence of the rapid growth of the density of states with energy. Introducing a high energy cutoff Λ, the transient dynamics during a time scale ≃1∕Λ describes the renormalization of the bare into a “quasiparticle” state which decays on longer time scales. During this early transient the decay law features Zeno behavior e{sup −(t∕t{sub Z}){sup 2}} with the Zeno time-scale t{sub Z}∝1∕Λ{sup 3∕2}. We introduce a dynamical renormalization framework that allows to separate consistently the dynamics of formation of the quasiparticle state and its decay on longer time scales by introducing a renormalization time scale along with alternative “schemes”. The survival probability obeys a renormalization group equation with respect to this scale. We find a transient suppression of the decay law for large Lorentz factor as a consequence of the narrowing of the phase space for decay different from the usual time dilation. In the presence of higher mass thresholds, the energy uncertainty associated with transient dynamics leads to an anti Zeno enhancement with a transient acceleration of the decay into heavier particles. There remains memory of the transient effects in the survival probability even at long time. We discuss possible consequences of these effects in cosmology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Lower hybrid wavepacket stochasticity revisited

Analysis is presented in support of the explanation in Ref. [1] for the observation of relativistic electrons during Lower Hybrid (LH) operation in EC pre-heated plasma at the WEGA stellarator [1,2]. LH power from the WEGA TE11 circular waveguide, 9 cm diameter, un-phased, 2.45 GHz antenna, is radiated into a B≅0.5 T, Ðœ„n{sub e}≅5×10{sup 17} 1/m{sup 3} plasma at T{sub e}≅10 eV bulk temperature with an EC generated 50 keV component [1]. The fast electrons cycle around flux or drift surfaces with few collisions, sufficient for randomizing phases but insufficient for slowing fast electrons down, and thus repeatedly interact with the rf field close to the antenna mouth, gaining energy in the process. Our antenna calculations reveal a standing electric field pattern at the antenna mouth, with which we formulate the electron dynamics via a relativistic Hamiltonian. A simple approximation of the equations of motion leads to a relativistic generalization of the area-preserving Fermi-Ulam (F-U) map [3], allowing phase-space global stochasticity analysis. At typical WEGA plasma and antenna conditions, the F-U map predicts an LH driven current of about 230 A, at about 225 W of dissipated power, in good agreement with the measurements and analysis reported in [1].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry

The generating function for the canonical transformation from the parallel canonical coordinates (s,p{sub ||}) to the action-angle coordinates (ζ, J) for trapped/passing guiding-center orbits in axisymmetric tokamak geometry is presented. Drawing on the analogy between the phase-space portraits of the librating/rotating pendulum and the trapped/passing guiding-center orbits, the generating function is expressed in terms of the Jacobi zeta function, which can then readily be used to obtain an explicit expression for the bounce-center transformation for trapped/passing-particle guiding-center orbits in axisymmetric tokamak geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗