Power-law Falloff Research Articles

Assessment of the near-Sun magnetic field of the 10 March 2022 coronal mass ejection observed by Solar Orbiter

Aims. We estimate the near-Sun axial magnetic field of a coronal mass ejection (CME) on 10 March 2022. Solar Orbiter’s in situ measurements, 7.8 degrees east of the Sun-Earth line at 0.43 AU, provided a unique vantage point, along with the WIND measurements at 0.99 AU. We determine a single power-law index from near-Sun to L1, including in situ measurements from both vantage points. Methods. We tracked the temporal evolution of the instantaneous relative magnetic helicity of the source active region (AR), NOAA AR 12962. By estimating the helicity budget of the pre-and post-eruption AR, we estimated the helicity transported to the CME. Assuming a Lundquist flux-rope model and geometrical parameters obtained through the graduated cylindrical shell (GCS) CME forward modelling, we determined the CME axial magnetic field at a GCS-fitted height. Assuming a power-law variation of the axial magnetic field with heliocentric distance, we extrapolated the estimated near-Sun axial magnetic field to in situ measurements at 0.43 AU and 0.99 AU. Results. The net helicity difference between the post-and pre-eruption AR is ( − 7.1 ± 1.2)×1041 Mx2, which is assumed to be bodily transported to the CME. The estimated CME axial magnetic field at a near-Sun heliocentric distance of 0.03 AU is 2067 ± 405 nT. From 0.03 AU to L1, a single power-law falloff, including both vantage points at 0.43 AU and 0.99 AU, gives an index −1.23 ± 0.18. Conclusions. We observed a significant decrease in the pre-eruptive AR helicity budget. Extending previous studies on inner-heliospheric intervals from 0.3 AU to ∼1 AU, referring to estimates from 0.03 AU to measurements at ∼1 AU. Our findings indicate a less steep decline in the magnetic field strength with distance compared to previous studies, but they align with studies that include near-Sun in situ magnetic field measurements, such as from Parker Solar Probe.

Critical and near-critical relaxation of holographic superfluids

We investigate the relaxation of holographic superfluids after quenches, when the end state is either tuned to be exactly at the critical point, or very close to it. By solving the bulk equations of motion numerically, we demonstrate that in the former case the system exhibits a power law falloff, as well as an emergent discrete scale invariance. The latter case is in the regime dominated by critical slowing down, and we show that there is an intermediate time range before the onset of late-time exponential falloff, where the system behaves similarly to the critical point with its power law falloff. We further postulate a phenomenological Gross-Pitaevskii-like equation (corresponding to model F of Hohenberg and Halperin) that is able to make quantitative predictions for the behavior of the holographic superfluid after near-critical quenches into the superfluid and normal phase. Intriguingly, all parameters of our phenomenological equation, which describes the nonlinear time evolution, may be fixed with information from the static equilibrium solutions and linear response theory. Published by the American Physical Society 2024

FarView: An in-situ manufactured lunar far side radio array concept for 21-cm Dark Ages cosmology

FarView is an early-stage concept for a large, low-frequency radio observatory, manufactured in-situ on the lunar far side using metals extracted from the lunar regolith. It consists of 100,000 dipole antennas in compact subarrays distributed over a large area but with empty space between subarrays in a core-halo structure. FarView covers a total area of ∼200 km2, has a dense core within the inner ∼36 km2, and a ∼power-law falloff of antenna density out to ∼14 km from the center. With this design, it is relatively easy to identify multiple viable build sites on the lunar far side. The science case for FarView emphasizes the unique capabilities to probe the unexplored Cosmic Dark Ages – identified by the 2020 Astrophysics Decadal Survey as the discovery area for cosmology. FarView will deliver power spectra and tomographic maps tracing the evolution of the Universe from before the birth of the first stars to the beginning of Cosmic Dawn, and potentially provide unique insights into dark matter, early dark energy, neutrino masses, and the physics of inflation. What makes FarView feasible and affordable in the timeframe of the 2030s is that it is manufactured in-situ, utilizing space industrial technologies. This in-situ manufacturing architecture utilizes Earth-built equipment that is transported to the lunar surface to extract metals from the regolith and will use those metals to manufacture most of the array components: dipole antennas, power lines, and silicon solar cell power systems. This approach also enables a long functional lifetime, by permitting servicing and repair of the observatory. The full 100,000 dipole FarView observatory will take 4–8 years to build, depending on the realized performance of the manufacturing elements and the lunar delivery scenario.

Majorana edge states in Kitaev chains of the BDI symmetry class

Majorana edge states in Kitaev chains possessing an effective time reversal symmetry with one fermionic site per unit cell are studied. For a semi-infinite chain the equations for the wave functions of Majorana zero modes can be reduced to a single Wiener-Hopf equation, which has an exact analytical solution. We use this solution to determine the asymptotic behaviors of the Majorana wave functions at large distances from the edge of the chain for several infinite-range models described in the literature with focus on a model with slow power-law falloff of pairing and hopping amplitudes. For these models we also determine the asymptotic behavior of the energy of the fermionic state composed of two Majorana modes in the limit of long (finite) Kitaev chains.

Chiral limit of a fermion-scalar (1/2)+ system in covariant gauges

The homogeneous Bethe-Salpeter equation (BSE) of a (1/2)$^+$ bound system, that has both fermionic and bosonic degrees of freedom, that we call a {\em mock nucleon}, is studied in Minkowski space, in order to analyse the chiral limit in covariant gauges. After adopting an interaction kernel built with a one-particle exchange, the $\chi$-BSE is numerically solved by means of the Nakanishi integral representation and light-front projection. Noteworthy, the chiral limit induces a scale-invariance of the model and consequently generates a wealth of striking features: i) it reduces the number of non trivial Nakanishi weight functions to only one; ii) the form of the surviving weight function has a factorized dependence on the two relevant variables, compact and non-compact one; iii) the coupling constant becomes an explicit function of the real exponent governing the power-law fall-off of the non trivial Nakanishi weight function. The thorough investigation at large transverse-momentum of light-front Bethe-Salpeter amplitudes, obtained with massive constituents, provides a confirmation of the expected universal power-law fall-off, with exponents predicted by our non-perturbative framework. Finally, one can shed light on the exponents that govern the approach to the upper extremum of the longitudinal-momentum fraction distribution function of the {\em mock nucleon}, when the coupling constant varies.

Kink solutions with power law tails

We present a comprehensive review about the various facets of kink solutions with a power law tail, which have received considerable attention during the last few years. This area of research is in its early stages; although several aspects have become clear by now, there are a number of issues which have only been partially understood or not understood at all. We first discuss the aspects which are reasonably well known and then address in some detail the issues which are only partially or not understood at all. We present a wide class of higher (than sixth) order field theory models admitting implicit kink as well as mirror kink solutions where the two tails facing each other have a power law or a power-tower type fall off, whereas the other two ends not facing each other could have either an exponential or a power law tail. The models admitting implicit kink solutions where the two ends facing each other have an exponential tail while the other two ends have a power law tail are also discussed. Moreover, we present several field theory models which admit explicit kink solutions with a power law fall off; we note that in all these polynomial models while the potential V(ϕ) is continuous, its derivative is discontinuous. We also discuss one of the most important and only partially understood issues of the kink–kink and the kink–antikink forces in case the tails facing each other have a power law fall off. Finally, we briefly discuss the kink–antikink collisions at finite velocity and present some open questions.

Quasinormal modes and late-time falloff of Finslerian black holes with cosmological constant

Quasinormal modes of scalar and electromagnetic field perturbations in Finslerian Reissner-Nordstr\"om black holes with a cosmological constant are investigated in this paper. We analyze the fundamental frequencies and dynamical evolution of quasinormal modes using the WKB approximation and finite difference method, respectively. Both approaches show that the periods of oscillation of quasinormal modes increase with higher Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ if the multipole quantum number $l\ensuremath{\ge}2$. Using the Prony method, we show that the results obtained from the finite difference method are consistent with the results obtained from the WKB approximation. Quasinormal modes of Finslerian black holes possess spectrum splitting, which reflects the fact that the spherical symmetry of the Finslerian black holes is broken. The effects of the Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ on the late-time tails of scalar and electromagnetic field perturbations are shown. The late-time tails of the Finslerian Reissner-Nordstr\"om black holes possess a power-law falloff. The power-law index has a discontinuous jump, while the Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ varies from 0 to nonzero. Such a fact reflects the fact that asymptotic-infinity behaviors of the Finslerian Reissner-Nordstr\"om black holes are different from their counterparts in general relativity.

Cylindrical paraxial optical beams described by the incomplete gamma function

An analytic formula for a certain type of a cylindrical beam, which might be called a $\ensuremath{\gamma}$ beam, has been derived directly from the paraxial equation and independently using the method of the Hankel transform formulated in our previous work [T. Rado\ifmmode \dot{z}\else \.{z}\fi{}ycki, Opt. Laser Technol. 147, 107670 (2022)]. The fundamental properties of this beam are analyzed and the parameters characterizing the beam shape are identified. The connection with Gaussian and elegant Laguerre-Gauss beams is demonstrated. In the plane perpendicular to the propagation axis, this beam is shown to display an expanding ring of high-energy concentration. At large radial distances the spatial profile exhibits a power-law falloff. The phase of the wave is also studied in this paper. Close to the symmetry axis it is shown to be typical of modes that exhibit vortex character, such as Gaussian beams of $n\mathrm{th}$ order, but at large distances it reveals a peculiar behavior distinct from Gaussian-type beams.

Skyrmion interactions and lattices in chiral magnets: analytical results

We study two-body interactions of magnetic skyrmions on the plane and apply them to a (mostly) analytic description of a skyrmion lattice. This is done in the context of the solvable line, a particular choice of a potential for magnetic anisotropy and Zeeman terms, where analytic expressions for skyrmions are available. The energy of these analytic single skyrmion solutions is found to become negative below a critical point, where the ferromagnetic state is no longer the lowest energy state. This critical value is determined exactly without the ambiguities of numerical simulations. Along the solvable line the interaction energy for a pair of skyrmions is repulsive with power law fall off in contrast to the exponential decay of a purely Zeeman potential term. Using the interaction energy expressions we construct an inhomogeneous skyrmion lattice state, which is a candidate ground states for the model in particular parameter regions. Finally we estimate the transition between the skyrmion lattice and an inhomogeneous spiral state.

Using QCD counting rules to identify the production of gluonium

The empirical identification of bound states of gluons has remained a central goal of hadron spectroscopy. We suggest an experimentally challenging, but model–independent way to assess which zero charge, isospin-zero mesons have a large gluonium light-front wavefunction component in the quark and gluon Fock space of QCD. Our method exploits QCD counting rules which relate the power-law fall-off of production amplitudes at high momentum transfer to the meson's twist (dimension minus spin of its minimum interpolating operators). Scalar 0+ glueballs composed of two valence gluons with zero internal orbital angular momentum have twist τ=2. In contrast, quark-antiquark |qq¯〉 scalar mesons have twist τ≥3 since they have nonzero orbital angular momentum, and multi-quark states such as |qqq¯q¯〉 tetraquarks yield twist τ≥4. Thus, the production cross section for both |qq¯〉 and |qqq¯q¯〉 mesons will be suppressed by at least one power of momentum transfer relative to glueball production. For example, in single inclusive particle hadroproduction AB→CX, the cross section for glueball production at high transverse momentum pT and fixed xT=2pTs will dominate higher twist mesons by at least two powers of pT.Similarly, in exclusive production processes at large CM energy and fixed CM angle, the glueball rate dominates by a power of s: we illustrate the method with a simple reaction, e−e+→ϕf0 where the f0 can be tested to be a glueball versus another type of scalar meson.

Inclusive production through AdS/CFT

It has been shown that AdS/CFT calculations can reproduce certain exclusive 2→2 cross sections in QCD at high energy, both for near-forward and for fixed-angle scattering. In this paper, we extend prior treatments by using AdS/CFT to calculate the inclusive single-particle production cross section in QCD at high center-of-mass energy. We find that conformal invariance in the UV restricts the cross section to have a characteristic power-law falloff in the transverse momentum of the produced particle, with the exponent given by twice the conformal dimension of the produced particle, independent of incoming particle types. We conclude by comparing our findings to recent LHC experimental data from ATLAS and ALICE, and find good agreement.

Hybrid MHD/PIC simulation of a deuterium gas puff z pinch

We present the hybrid MHD/PIC simulations of the time evolution of a deuterium gas puff z pinch. Recent experiments with 3-MA current pinches [6] made in a novel configuration have shown that the neutron yields can reach 3.6×1012. It was shown that the observed neutron spectra could be explained by a suprathermal distribution of deuterons with a power law fall off in the ion energy distribution function at large energy. In order to perform the numerical simulation of gas puff z pinch a new hybrid model was developed. The described hybrid model treats the electrons as a massless fluid and ions as macroparticles. The macroparticle dynamic is calculated with the use of PIC method. Ion-ion Coulomb collision is considered with the use of MC method. In the model simulation, in the configuration close to described in [6], it was obtained the neutron yields up to 1.2×1012. Most neutrons are not thermonuclear. This level of the neutron yield is reached only when a strongly nonuniform neck-like constriction of z-pinch plasma occurs. In this case, the obtained deuteron spectra (with energy up to several tens MeV) have suprathermal high energy tail. These simulations demonstrate the utility of the developed hybrid model for the z-pinch simulation.

Meson/baryon/tetraquark supersymmetry from superconformal algebra and light-front holography

Superconformal algebra leads to remarkable connections between the masses of mesons and baryons of the same parity — supersymmetric relations between the bosonic and fermionic bound states of QCD. Supercharges connect the mesonic eigenstates to their baryonic superpartners, where the mesons have internal angular momentum one unit higher than the baryons: [Formula: see text] The dynamics of the superpartner hadrons also match; for example, the power-law fall-off of the form factors are the same for the mesonic and baryonic superpartners, in agreement with twist counting rules. An effective supersymmetric light-front Hamiltonian for hadrons composed of light quarks can be constructed by embedding superconformal quantum mechanics into AdS space. This procedure also generates a spin–spin interaction between the hadronic constituents. A specific breaking of conformal symmetry inside the graded algebra determines a unique quark-confining light-front potential for light hadrons in agreement with the soft-wall AdS/QCD approach and light-front holography. Only one mass parameter [Formula: see text] appears; it sets the confinement mass scale, a universal value for the slope of all Regge trajectories, the nonzero mass of the proton and other hadrons in the chiral limit, as well as the length scale which underlies their structure. The mass for the pion eigenstate vanishes in the chiral limit. When one includes the constituent quark masses using the Feynman–Hellman theorem, the predictions are consistent with the empirical features of the light-quark hadronic spectra. Our analysis can be consistently applied to the excitation spectra of the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] meson families as well as to the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] baryons. We also predict the existence of tetraquarks which are degenerate in mass with baryons with the same angular momentum. The mass-squared of the light hadrons can be expressed in a universal and frame-independent decomposition of contributions from the constituent kinetic energy, the confinement potential, and spin–spin contributions. We also predict features of hadron dynamics, including hadronic light-front wave functions, distribution amplitudes, form factors, valence structure functions and vector meson electroproduction phenomenology. The mass scale [Formula: see text] can be connected to the parameter [Formula: see text] in the QCD running coupling by matching the nonperturbative dynamics, as described by the light-front holographic approach to the perturbative QCD regime. The result is an effective coupling defined at all momenta. The matching of the high and low momentum-transfer regimes determines a scale [Formula: see text] proportional to [Formula: see text] which sets the interface between perturbative and nonperturbative hadron dynamics. The use of [Formula: see text] to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the scheme-independent Principle of Maximal Conformality (PMC) procedure for setting renormalization scales, can greatly improve the precision of perturbative QCD predictions.

Enhancement of high-order harmonic generation in intense laser interactions with solid density plasma by multiple reflections and harmonic amplification

High order harmonic generation (HHG) from laser solid-density plasma interactions is considered as a promising way to generate bright and ultrashort burst of x-rays. One of the key issues for HHG is the low conversion efficiency due to a power law fall off in harmonic intensity. Here, we explore a possible mechanism for HHG enhancement by reflecting an intense laser pulse multiple times between two plasma surfaces. We find that HHG can be nonlinearly enhanced by orders of magnitude through multiple reflections compared with a single reflection. We argue this enhancement is due to the non-linear combination of the relativistically oscillating plasma mirror and the harmonic-rich pulse generated in preceding reflections. This mechanism should allow moderate power laser systems to efficiently generate coherent, ultrashort bursts of soft x-rays.

General relativity and the cuprates

We add a periodic potential to the simplest gravitational model of a superconductor and compute the optical conductivity. In addition to a superfluid component, we find a normal component that has Drude behavior at low frequency followed by a power law fall-off. Both the exponent and coefficient of the power law are temperature independent and agree with earlier results computed above $T_c$. These results are in striking agreement with measurements on some cuprates. We also find a gap $\Delta = 4.0\ T_c$, a rapidly decreasing scattering rate, and "missing spectral weight" at low frequency, all of which also agree with experiments.

Asymptotic analysis of the Boltzmann equation for dark matter relics

This paper presents an asymptotic analysis of the Boltzmann equations (Riccati differential equations) that describe the physics of thermal dark-matter-relic abundances. Two different asymptotic techniques are used, boundary-layer theory, which makes use of asymptotic matching, and the delta expansion, which is a powerful technique for solving nonlinear differential equations. Two different Boltzmann equations are considered. The first is derived from general relativistic considerations and the second arises in dilatonic string cosmology. The global asymptotic analysis presented here is used to find the long-time behavior of the solutions to these equations. In the first case, the nature of the so-called freeze-out region and the post-freeze-out behavior is explored. In the second case, the effect of the dilaton on cold dark-matter abundances is calculated and it is shown that there is a large-time power-law fall off of the dark-matter abundance.

Neutron scattering measurements in RbMnF3: A test of spin-wave-region theories at low temperatures and critical behavior near TN

With the discovery of magnetic ordering in RbMnF3, this unique antiferromagnetic system was recognized as a prime case for a test of conventional spin-wave theory (CSWT) because of its negligibly small anisotropy and its simple, cubic structure. CSWT predicts a simple T2 power-law fall-off of the sublattice magnetization. Yet to this day, no stringent tests have been made of this prediction. Seiden [(Phys. Lett. 28 A, 239 (1968)] deduced a T3 low-temperature behavior on the basis of antiferromagnetic resonance measurements, concluding that CSWT was not supported. We have recently carried out neutron scattering measurements of both single-crystal and powdered samples of RbMnF3 in order to test for CSWT, Seiden’s result, and two other more recent semiempirical spin-wave schemes, and we present an analysis of the results. Measurements in the critical regime gave values of the critical exponent β and of TN that are in agreement with previous measurements.

Hydrodynamic long-time tails from Anti de Sitter space

For generic field theories at finite temperature, a power-law falloff of correlation functions of conserved currents at long times is a prediction of non-linear hydrodynamics. We demonstrate, through a one-loop computation in Einstein gravity in Anti de Sitter space, that this effect is reproduced by the dynamics of black hole horizons. The result is in agreement with the gauge-gravity correspondence.

Kinetic simulation of thermonuclear-neutron production by a 107-A deuterium Z pinch

Fully kinetic simulations have demonstrated that at sufficiently high currents, half of the neutrons produced by a deuterium Z-pinch are thermonuclear in origin. At 150-kA pinch current, O. A. Anderson et al. [Phys. Rev. 110, 1375 (1958)] clearly shows that essentially all of the neutrons produced by a deuterium pinch are not thermonuclear, but are initiated by an instability that creates beam-target neutrons. Since this paper, many subsequent authors have supported this result while others have claimed that pinch neutrons are, on the contrary, thermonuclear. To resolve this issue, fully kinetic, collisional, and electromagnetic simulations of the complete time evolution of a deuterium pinch have been performed. The simulations were performed with the implicit particle-in-cell code LSP, as described in D. R. Welch et al. [Phys. Rev. Lett. 103, 255002 (2009)]. At 106 -A pinch currents, most of the neutrons are, indeed, beam-target in origin. At 15-MA current, half of the neutrons are thermonuclear and half are beam-target driven by instabilities that produce a power law fall off in the ion energy distribution function at large energy. Simulation results suggest that from 7- to 15-MA current, the fraction of thermonuclear neutrons is not sensitive to current and that the strong dependence of neutron yield on current will continue at currents greater than 15 MA.

Generalized Statistical Models of Voids and Hierarchical Structure in Cosmology

Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution which contains a parameter a. The parameter is related to the Levy index alpha and the Fisher critical exponent tau, the latter describing the power law fall off of clumps of matter around a phase transition. The parametera, exponent tau, or index alpha can be obtained from properties of a void scaling function. A stochastic probability variable is introduced into a statistical model which represent the adhesive growth of galaxy structure. For p 1/2, an adhesive growth can go on indefinitely thereby forming an infinite supercluster. At p=1/2 a scale free power law distribution for the galaxy count distribution is present. The stochastic description also leads to consequences that have some parallels with cosmic string results, percolation theory and phase transitions.