Regions Of Phase Space Research Articles

Search for axion(-like) particles in heavy-ion collisions

We propose a novel way to search for axion(-like) particles in heavy-ion collisions using prompt photons as the probe and the property of conversion between photon and axion(-like) particles under a strong magnetic field generated in the non-central collisions. The expected result reveals that a new phase space region of the coupling constant for photon and axion(-like) particles can be covered in the future high energy nuclear colliders.

Harnessing interpretable and unsupervised machine learning to address big data from modern X-ray diffraction

The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern X-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big datasets when a comprehensive analysis is beyond human reach. We report the development of an unsupervised machine learning approach, X-ray diffraction (XRD) temperature clustering (X-TEC), that can automatically extract charge density wave order parameters and detect intraunit cell ordering and its fluctuations from a series of high-volume X-ray diffraction measurements taken at multiple temperatures. We benchmark X-TEC with diffraction data on a quasi-skutterudite family of materials, (CaxSr[Formula: see text])3Rh4Sn13, where a quantum critical point is observed as a function of Ca concentration. We apply X-TEC to XRD data on the pyrochlore metal, Cd2Re2O7, to investigate its two much-debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic-scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC-revealed selection rules that the Cd and Re displacements are approximately equal in amplitude but out of phase. This discovery reveals a previously unknown involvement of [Formula: see text] Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on the fly.

Modeling colloidal interactions that predict equilibrium and non-equilibrium states.

Modulating the interaction potential between colloids suspended in a fluid can trigger equilibrium phase transitions as well as the formation of non-equilibrium "arrested states," such as gels and glasses. Faithful representation of such interactions is essential for using simulation to interrogate the microscopic details of non-equilibrium behavior and for extrapolating observations to new regions of phase space that are difficult to explore in experiments. Although the extended law of corresponding states predicts equilibrium phases for systems with short-ranged interactions, it proves inadequate for equilibrium predictions of systems with longer-ranged interactions and for predicting non-equilibrium phenomena in systems with either short- or long-ranged interactions. These shortcomings highlight the need for new approaches to represent and disambiguate interaction potentials that replicate both equilibrium and non-equilibrium phase behavior. In this work, we use experiments and simulations to study a system with long-ranged thermoresponsive colloidal interactions and explore whether a resolution to this challenge can be found in regions of the phase diagram where temporal effects influence material state. We demonstrate that the conditions for non-equilibrium arrest by colloidal gelation are sensitive to both the shape of the interaction potential and the thermal quench rate. We exploit this sensitivity to propose a kinetics-based algorithm to extract distinct arrest conditions for candidate potentials that accurately selects between potentials that differ in shape but share the same predicted equilibrium structure. The algorithm selects the candidate that best matches the non-equilibrium behavior between simulation and experiments. Because non-equilibrium behavior in simulation is encoded entirely by the interparticle potential, the results are agnostic to the particular mechanism(s) by which arrest occurs, and so we expect our method to apply to a range of arrested states, including gels and glasses. Beyond its utility in constructing models, the method reveals that each potential has a quantitatively distinct arrest line, providing insight into how the shape of longer-ranged potentials influences the conditions for colloidal gelation.

Orbital stability analysis of hypothetical Earth-mass and Luna-mass moons in the Sagarmatha (HD 100777) star system

Abstract Six of the solar system planets have 150 confirmed moons (Earth—1, Mars—2, Jupiter—53, Saturn—53, Uranus—27, Neptune—14) and seven of them (Ganymede, Titan, Callisto, Io, the Moon, Europa, Triton) have masses >0.001 $M_\oplus$. However, no exomoons have yet been discovered despite the successful detection of ∼5000 exoplanets. We can infer, based on the solar system planets, that these exoplanets are capable of hosting one or more exomoons. In this paper, we study the possible existence of hypothetical Earth-mass and Luna-mass moons orbiting the Jupiter-mass planet, Laligurans (HD 100777b) in the Sagarmatha (HD 100777) star system by means of orbital stability. We apply long-term orbital integrations and the MEGNO (mean exponential growth of nearby orbits) chaos indicator to study the orbital stability of the moons and predict a phase-space region comprising periodic, chaotic, and unstable orbits. The phase spaces primarily constitute the moon's semimajor axis, which extends from the host planet's Roche radius to the Hill radius, and full range of eccentricity. Specific points are picked from three different regions of the MEGNO map and run as single-orbit integration for up to 10 billion periods of the innermost orbit. Furthermore, the lifetime and maximum eccentricity maps are generated from the direct integration to inspect the stable and unstable orbital configurations. The analyses of these maps, with the aid of time-series plots, show that both moons maintain stable orbits in the low-eccentricity regime and semimajor axis between the Roche limit and 28.4% of the Hill radius of the planet.

Helioscope for gravitationally bound millicharged particles

Particles may be emitted efficiently from the solar interior if they are sufficiently light and weakly coupled to the solar plasma. In a narrow region of phase space, they are emitted with velocities smaller than the escape velocity of the Solar System, thereby populating a gravitationally bound density that can accumulate over the solar lifetime, referred to as a ``solar basin.'' Detection strategies that can succeed in spite of (or even be enhanced by) the low particle velocities are therefore poised to explore new regions of parameter space when taking this solar population into account. Here we identify ``direct deflection'' as a powerful method to detect such a population of millicharged particles. This approach involves distorting the local flow of gravitationally bound millicharges with an oscillating electromagnetic field and measuring these distortions with a resonant $LC$ circuit. Since it is easier to distort the flow of slowly moving particles, the signal is parametrically enhanced by the small solar escape velocity near Earth. The proposed setup can probe couplings an order of magnitude smaller than other methods for millicharge masses ranging from 100 to 100 eV and can operate concurrently as a search for sub-GeV millicharged dark matter. The signal power scales as the millicharge coupling to the eighth power, meaning that even with conservative assumptions, direct deflection could begin to explore new regions of parameter space. We also highlight novel features of millicharge solar basins, including those associated with the phase-space distribution and the possibility for the occupation number to vastly exceed that of a thermal distribution.

HEJ 2.1: High-energy resummation with vector bosons and next-to-leading logarithms

We present version 2.1 of the High Energy Jets (HEJ) event generator for hadron colliders. HEJ is a Monte Carlo generator for processes at high energies with multiple well-separated jets in the final state. To achieve accurate predictions, conventional fixed-order perturbative QCD is supplemented with an all-order resummation of large high-energy logarithms. The new version 2.1 now supports processes with final-state leptons originating from a charged or neutral vector boson together with multiple jets, in addition to processes available in earlier versions. Furthermore, the all-order resummation is extended to include an additional gauge-invariant class of subdominant logarithmic corrections. HEJ 2.1 can be obtained from https://hej.hepforge.org. New version program summaryProgram Title:HEJ.CPC Library link to program files:https://doi.org/10.17632/24c9mb6pf9.2Licensing provisions: GPLv2 or later.Programming language: C++.Journal reference of previous version: Comput. Phys. Commun. 245 (2019) 106832.Does the new version supersede the previous version?: YesReasons for the new version: Support for further scattering processes and inclusion of additional corrections.Summary of revisions: This release adds support for the production of two final-state leptons originating from a charged or neutral vector boson together with multiple jets. Resummation is extended to include next-to-leading logarithmic corrections connected to the emission of additional quark-antiquark pairs.Nature of problem: Conventional event generators for high-energy colliders are based on fixed-order perturbation theory, which converges poorly in regions of phase space with large invariant masses between jets. Reliable predictions in these regions are of general interest, and particularly important whenever cuts relevant to weak-boson fusion or weak-boson scattering are applied.Solution method: The perturbative description can be amended by resumming the high-energy logarithms associated with large invariant masses to all orders in perturbation theory. HEJ 2 implements this resummation following the High Energy Jets framework. Using HEJ 2 in conjunction with a conventional event generator allows one to obtain reliable predictions for processes involving multiple jets in high-energy regions of phase space.Additional comments including restrictions and unusual features: The current version implements multi-jet processes with at most a single lepton pair or Higgs boson in the final state. Matching to fixed-order perturbation theory is currently restricted to leading order.

Applicability of semiclassical methods for modeling laser-enhanced fusion rates in a realistic setting

In the context of the potential laser-induced enhancement to the rates of ${\mathrm{DHe}}^{3}$ and DT fusion, we discuss the frequently-used Wentzel-Kramers-Brillouin (WKB) method and the imaginary-time method (ITM). For static external electric fields, we find that these methods predict significant enhancement to the fusion cross section for electric-field strengths $>{10}^{14}$ V/m, especially at low values ($\ensuremath{\approx}$ keV) for the enter-of-mass (CoM) energy. When considering dynamic electric fields, this enhancement can be amplified by considering increased photon frequencies. However, we also provide a review of the region of laser-parameter phase space where these semiclassical methods are applicable. We conclude that this allowable region decreases for higher photon frequencies in conjunction with lower values for the electric-field strength, motivating the need for future experiments to test the predictions of these methods and their ranges of validity.

Brownian bridges for stochastic chemical processes-An approximation method based on the asymptotic behavior of the backward Fokker-Planck equation.

A Brownian bridge is a continuous random walk conditioned to end in a given region by adding an effective drift to guide paths toward the desired region of phase space. This idea has many applications in chemical science where one wants to control the endpoint of a stochastic process-e.g., polymer physics, chemical reaction pathways, heat/mass transfer, and Brownian dynamics simulations. Despite its broad applicability, the biggest limitation of the Brownian bridge technique is that it is often difficult to determine the effective drift as it comes from a solution of a Backward Fokker-Planck (BFP) equation that is infeasible to compute for complex or high-dimensional systems. This paper introduces a fast approximation method to generate a Brownian bridge process without solving the BFP equation explicitly. Specifically, this paper uses the asymptotic properties of the BFP equation to generate an approximate drift and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. Because such a procedure avoids the solution of the BFP equation, we show that it drastically accelerates the generation of conditioned random walks. We also show that this approach offers reasonable improvement compared to other sampling approaches using simple bias potentials.

Driven toroidal helix as a generalization of the Kapitza pendulum.

We explore a model system consisting of a particle confined to move along a toroidal helix while being exposed to a static potential as well as a driving force due to a harmonically oscillating electric field. It is shown that in the limit of a vanishing helix radius, the governing equationsof motion coincide with those of the well-known Kapitza pendulum-a classical pendulum with oscillating pivot-implying that the driven toroidal helix represents a corresponding generalization. It is shown that the two dominant static fixed points present in the Kapitza pendulum are also present for a finite helix radius. The dependence of the stability of these two fixed points on the helix radius, the driving amplitude, and the static potential are analyzed analytically. These analytical results are subsequently compared to results corresponding of numerical simulations. Additionally, the most prominent deviations of the driven helix from the Kapitza pendulum with respect to the resulting phase space are investigated and analyzed in some detail. These effects include an unusual transition to chaos and an effective directed transport due to the simultaneous presence of multiple chaotic phase space regions.

Periodic orbits in the 1:2:3 resonant chain and their impact on the orbital dynamics of the Kepler-51 planetary system

Aims. Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that introduce chaos into the evolution of the system on especially shorter or longer timescales. We propose a study of the dynamics of such systems by exploring particular regions in phase space. Methods. We exemplify our method by studying the long-term orbital stability of the three-planet system Kepler-51 and either favor or constrain its data. It is a dual process which breaks down in two steps: the computation of the families of periodic orbits in the 1:2:3 resonant chain and the visualization of the phase space through maps of dynamical stability. Results. We present novel results for the general four-body problem. Stable periodic orbits were found only in the low-eccentricity regime. We demonstrate three possible scenarios safeguarding Kepler-51, each followed by constraints. Firstly, there are the 2/1 and 3/2 two-body MMRs, in which eb < 0.02, such that these two-body MMRs last for extended time spans. Secondly, there is the 1:2:3 three-body Laplace-like resonance, in which ec < 0.016 and ed < 0.006 are necessary for such a chain to be viable. Thirdly, there is the combination comprising the 1/1 secondary resonance inside the 2/1 MMR for the inner pair of planets and an apsidal difference oscillation for the outer pair of planets in which the observational eccentricities, eb and ec, are favored as long as ed ≈ 0. Conclusions. With the aim to obtain an optimum deduction of the orbital elements, this study showcases the need for dynamical analyses based on periodic orbits performed in parallel to the fitting processes.

Stellar triples on the edge

Context. Hierarchical triple stars are ideal laboratories for studying the interplay between orbital dynamics and stellar evolution. Both mass loss from stellar winds and strong gravitational perturbations between the inner and outer orbit cooperate to destabilise triple systems. Aims. Our current understanding of the evolution of unstable triple systems is mainly built upon results from extensive binary-single scattering experiments. However, destabilised hierarchical triples cover a different region of phase space. Therefore, we aim to construct a comprehensive overview of the evolutionary pathways of destabilised triple-star systems. Methods. Starting from generic initial conditions, we evolved an extensive set of hierarchical triples using the code TRES, combining secular dynamics and stellar evolution. We detected those triples that destabilise due to stellar winds and/or gravitational perturbations. Their evolution was continued with a direct N-body integrator coupled to stellar evolution. Results. The majority of triples (54–69%) preserve their hierarchy throughout their evolution, which is in contradiction with the commonly adopted picture that unstable triples always experience a chaotic, democratic resonant interaction. The duration of the unstable phase was found to be longer than expected (103 − 4 crossing times, reaching up to millions), so that long-term stellar evolution effects cannot be neglected. The most probable outcome is dissolution of the triple into a single star and binary (42–45%). This occurs through the commonly known democratic channel, during which the initial hierarchy is lost and the lightest body usually escapes, but also through a hierarchical channel, during which the tertiary is ejected in a slingshot, independent of its mass. Collisions are common (13–24% of destabilised triples), and they mostly involve the two original inner binary components still on the main sequence (77–94%). This contradicts the idea that collisions with a giant during democratic encounters dominate (only 5–12%). Together with collisions in stable triples, we find that triple evolution is the dominant mechanism for stellar collisions in the Milky Way. Lastly, our simulations produce runaway and walk-away stars with speeds up to several tens of km/s, with a maximum of a few 100 km s−1. We suggest that destabilised triples can explain – or at least alleviate the tension behind – the origin of the observed (massive) runaway stars. Conclusions. A promising indicator for distinguishing triples that will follow the democratic or hierarchical route, is the relative inclination between the inner and outer orbits. Its influence can be summed up in two rules of thumb: (1) prograde triples tend to evolve towards hierarchical collisions and ejections, and (2) retrograde triples tend to evolve towards democratic encounters and a loss of initial hierarchy, unless the system is compact, which experience collision preferentially. The trends found in this work complement those found previously from binary-single scattering experiments, and together they will help to generalise and improve our understanding on the evolution of unstable triple systems of various origins.

Nonlinear adiabatic electron plasma waves: I. General theory and nonlinear frequency shift

This paper provides a complete self-consistent nonlinear theory for electron plasma waves, within the framework of the adiabatic approximation. The theory applies whatever the variations of the wave amplitude provided that they are slow enough, and it is also valid when the plasma is inhomogeneous and non-stationary. Moreover, it accounts for: (i) the geometrical jump in action resulting from separatrix crossing; (ii) the continuous change in phase velocity making the wave frame non-inertial; (iii) the harmonic content of the scalar potential; (iv) a non-zero vector potential; (v) the transition probabilities from one region of phase space to the other when an orbit crosses the separatrix; and (vi) the possible change in direction of the wavenumber. The relative importance of each of the aforementioned effects is discussed in detail, based on the derivation of the nonlinear frequency shift. This allows us to specify how the general formalism may be simplified, depending on the value of the wavenumber normalized to the Debye length. Specific applications of our theory are reported in Paper II.

Single π0 production in μe scattering at MUonE

The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision prediction in radiative corrections to the μe scattering as well as for robust quantitative estimates of all possible background processes. In this letter, the contribution due to the emission of a neutral pion through the process μe→μeπ0 is studied and its numerical impact is discussed in different phase space configurations by means of the upgraded Monte Carlo event generator MESMER. In fact, single π0 production could be a source of reducible background for the measurement of the QED running coupling constant at MUonE and it could be also an important background for possible New Physics searches at MUonE involving 2→3 processes, in phase space regions complementary to the ones characteristic of the elastic μe scattering.

Search for a right-handed W boson and a heavy neutrino in proton-proton collisions at sqrt{s} = 13 TeV

A search is presented for a right-handed W boson (WR) and a heavy neutrino (N), in a final state consisting of two same-flavor leptons (ee or μμ) and two quarks. The search is performed with the CMS experiment at the CERN LHC using a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 138 fb−1. The search covers two regions of phase space, one where the decay products of the heavy neutrino are merged into a single large-area jet, and one where the decay products are well separated. The expected signal is characterized by an excess in the invariant mass distribution of the final-state objects. No significant excess over the standard model background expectations is observed. The observations are interpreted as upper limits on the product of WR production cross sections and branching fractions assuming that couplings are identical to those of the standard model W boson. For N masses mN equal to half the WR mass {m}_{{mathrm{W}}_{mathrm{R}}} (mN = 0.2 TeV), {m}_{{mathrm{W}}_{mathrm{R}}} is excluded at 95% confidence level up to 4.7 (4.8) and 5.0 (5.4) TeV for the electron and muon channels, respectively. This analysis provides the most stringent limits on the WR mass to date.

Universal structure of radiative QED amplitudes at one loop

We present two novel results about the universal structure of radiative QED amplitudes in the soft and in the collinear limit. On the one hand, we extend the well-known Low-Burnett-Kroll theorem to the one-loop level and give the explicit relation between the radiative and non-radiative amplitude at subleading power in the soft limit. On the other hand, we consider a factorisation formula at leading power in the limit where the emitted photon becomes collinear to a light fermion and provide the corresponding one-loop splitting function. In addition to being interesting in their own right these findings are particularly relevant in the context of fully-differential higher-order QED calculations. One of the main challenges in this regard is the numerical stability of radiative contributions in the soft and collinear regions. The results presented here allow for a stabilisation of real­virtual amplitudes in these delicate phase-space regions by switching to the corresponding approximation without the need of explicit computations.

Effective Phase Space Representation of the Quantum Dynamics of Vibrational Predissociation of the ArBr2(B,ν =16···25) Complex.

We perform trajectory-based simulations of the vibrational predissociation of the ArBr2(B,ν=16···25) van der Waals triatomic complex, constrained to the T-shape geometry. To this aim, we employ a 2-fold mapping of the quantum dynamics into classical-like dynamics in an extended phase space. The effective phase space comprises two distinct sets of degrees of freedom, namely a collection of coupled harmonic oscillators and an ensemble of quantum trajectories. The time evolution of these variables represent bound and unbound motions of the quantum system, respectively. Quantum trajectories are propagated within the interacting trajectory representation. The comparison between the lifetimes of the predissociating complexes computed using the trajectory-based approach and the experimental results available for the target systems indicates that the present method is competitive with wavepacket propagation techniques. The competition between several simultaneous vibrational relaxation pathways was found to have a direct impact on the time scales of vibrational predissociation. Likewise, the analysis of the time evolution of the trajectories reveals the existence of regions in the effective phase space where transitions to vibrational states of higher energy are more likely to occur. The size and location of these regions influence the transient vibrational distributions and therefore the computed lifetimes. Furthermore, the mechanisms of energy redistribution along the dissociation coordinate are analyzed.

Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem

Consider the Restricted Planar Circular 3 Body Problem. If the trajectory of the body of zero mass is defined for all time, it can have the following four types of asymptotic motion when time tends to infinity forward or backward in time: bounded, parabolic (goes to infinity with asymptotic zero velocity), hyperbolic (goes to infinity with asymptotic positive velocity) or oscillatory (the position of the body is unbounded but goes back to a compact region of phase space for a sequence of arbitrarily large times). We consider realistic mass ratio for the Sun-Jupiter pair and Jacobi constant which allows the massless body to cross Jupiter's orbit. This is a non-perturbative regime. We prove the existence of all possible combinations of past and future final motions. In particular, we obtain the existence of oscillatory motions. All the constructed trajectories cross the orbit of Jupiter but avoid close encounters with it.The proof relies on analyzing the stable and unstable invariant manifolds of infinity and their intersections. We construct orbits shadowing these invariant manifolds by the method of correctly aligned windows. The proof is computer assisted.

Regions without invariant tori of given class for the planar circular restricted three-body problem

A method to establish regions of phase space through which pass no invariant tori transverse to a given direction field is applied to the planar circular restricted three-body problem. Implications for the location of stable orbits for planets around a binary star are deduced. It is expected that lessons learnt from this problem will be useful for applications of the method to other contexts such as flux surfaces for magnetic fields, guiding centre motion in magnetic fields, and classical models of chemical reaction dynamics.

Toward an integrated platform for characterizing laser-driven, isochorically heated plasmas with 1 µm spatial resolution.

Warm dense matter is a region of phase space that is of high interest to multiple scientific communities ranging from astrophysics to inertial confinement fusion. Further understanding of the conditions and properties of this complex state of matter necessitates experimental benchmarking of the current theoretical models. We discuss the development of an x-ray radiography platform designed to measure warm dense matter transport properties at large laser facilities such as the OMEGA Laser Facility. Our platform, Fresnel diffractive radiography, allows for high spatial resolution imaging of isochorically heated targets, resulting in notable diffractive effects at sharp density gradients that are influenced by transport properties such as thermal conductivity. We discuss initial results, highlighting the capabilities of the platform in measuring diffractive features with micrometer-level spatial resolution.

Two-loop hexa-box integrals for non-planar five-point one-mass processes

We present the calculation of the three distinct non-planar hexa-box topologies for five-point one-mass processes. These three topologies are required to obtain the two-loop virtual QCD corrections for two-jet-associated W, Z or Higgs-boson production. Each topology is solved by obtaining a pure basis of master integrals and efficiently constructing the associated differential equation with numerical sampling and unitarity-cut techniques. We present compact expressions for the alphabet of these non-planar integrals, and discuss some properties of their symbol. Notably, we observe that the extended Steinmann relations are in general not satisfied. Finally, we solve the differential equations in terms of generalized power series and provide high-precision values in different regions of phase space which can be used as boundary conditions for subsequent evaluations.