Phase-space Distribution Research Articles

Validation of three-dimensional simulation of beam transport using linear accelerator based on measured phase-space distributions

Validation of three-dimensional simulation of beam transport using linear accelerator based on measured phase-space distributions

Thermostat-induced artificial lane formation in non-equilibrium molecular dynamics.

While most thermostats in molecular dynamics are designed for equilibrium systems, their extension to non-equilibrium simulations has little theoretical justification. In the literature, an artifact referred to as "lane formation" was discovered; however, its cause remained unclear and was simply attributed to a constraint on velocity fluctuations or non-ergodicity in thermostats. In addition, global deterministic thermostatted dynamics was found to exhibit unceasing phase-space compression in steady states, incompatible with their expected stationary distributions and Gibbs entropy, which was mistakenly perceived as inescapable. In this work, we pinpoint that the dynamical cause of artificial lane formation is a stable fixed point in the momentum space induced by improper velocity rescaling, which produces effective repulsion between different species in a color flow, drains transverse kinetic energy and generates the unceasing compression. This artifact is deeply rooted in global deterministic thermostats, such as the Nosé-Hoover dynamics and configurational thermostat. With proper rescaling, the Langevin thermostat completely eliminates artificial lane formation and exemplifies how incompressible phase space and stationary distributions can be retained for non-equilibrium steady states.

Selecting Initial Conditions for Trajectory-Based Nonadiabatic Simulations.

ConspectusPhotochemical reactions have always been the source of a great deal of mystery. While classified as a type of chemical reaction, no doubts are allowed that the general tenets of ground-state chemistry do not directly apply to photochemical reactions. For a typical chemical reaction, understanding the critical points of the ground-state potential (free) energy surface and embedding them in a thermodynamics framework is often enough to infer reaction yields or characteristic time scales. A general working principle is that the energy profile along the minimum energy paths provides the key information to characterize the reaction. These well-developed concepts, unfortunately, rarely stretch to processes involving the formation of a nonstationary state for a molecular system after light absorption.Upon photoexcitation, a molecule is likely to undergo internal conversion processes, that is, changes of electronic states mediated by couplings between nuclear and electronic motion, precisely what the celebrated Born-Oppenheimer approximation neglects. These coupled electron-nuclear processes, coined nonadiabatic processes, allow for the molecule to decay from one electronic state to the other nonradiatively. Understanding the intricate nonadiabatic dynamics is pivotal to rationalizing and predicting the outcome of a molecular photoexcitation and providing insights for experiments conducted, for example, in advanced light sources such as free-electron lasers.Nowadays, most simulations in nonadiabatic molecular dynamics are based on approximations that invoke a near-classical depiction of the nuclei. This reliance is due to practical constraints, and the classical equations of motion for the nuclei must be supplemented by techniques such as surface hopping to account for nonadiabatic transitions between electronic states. A critical but often overlooked aspect of these simulations is the selection of initial conditions, specifically the choice of initial nuclear positions and momenta for the nonadiabatic dynamics, which can significantly influence how well the simulations mimic real quantum systems across various experimental scenarios. The conventional approach for generating initial conditions for nonadiabatic dynamics typically maps the initial state onto a nuclear phase space using a Wigner quasiprobability function within a harmonic approximation, followed by a second approximation where the molecule undergoes a sudden excitation.In this Account, we aim to warn the experienced or potential user of nonadiabatic molecular dynamics about the possible limitations of this strategy for initial-condition generation and its inability to accurately describe the photoexcitation of a molecule. More specifically, we argue that the initial phase-space distribution can be more accurately represented through molecular dynamics simulations by using a quantum thermostat. This method offers a robust framework that can be applied to large, flexible, or even solvated molecular systems. Furthermore, the reliability of this strategy can be benchmarked against more rigorous approaches such as path integral molecular dynamics. Additionally, the commonly used sudden approximation, which assumes a vertical and sudden excitation of a molecule, rarely reflects the excitation triggered by laser pulses used in actual photochemical and spectroscopic experiments. We discuss here a more general approach that can generate initial conditions for any type of laser pulse. We also discuss strategies to tackle excitation triggered by a continuous-wave laser.

Neutrinos of magnetorotational supernovae

The neutrino dynamics in hot and dense magnetized matter corresponding to a supernova explosion is considered. It is shown that accounting for fluctuations during interaction of neutrinos with matter leads to the Fokker–Planck equation for the dynamics of the phase space distribution function. The addition to the energy transfer component of the kinetic equation is determined by straggling in neutrino collisions with a magnetized nucleon gas caused by the neutral current Gamow–Teller interaction. When accounting for the effect of fluctuations, the switching of acceleration and stopping regimes in neutrino evolution is evident for average energy. The effect of fluctuations leads to an additional increase in the hardness of the neutrino spectra. It is shown that the high-energy component of the electron antineutrino flux is enhanced in addition due to the effect of neutrino oscillations. Such a strengthening of the spectrum hardness is especially noticeable in the case of the inverted mass ordering and makes the signal more registrable by ground-based detectors. The possibilities of detecting supernova neutrinos by KM3NeT and Baikal-GVD observatories are discussed. The sensitivity of counting rate to the mass ordering is demonstrated to increase at growing difference in the hardness of energy spectra for various flavors.

QCD axion: Some like it hot

We compare the quantum chromodynamics (QCD) axion phase-space distribution from unitarized next-to-leading order chiral perturbation theory with the one extracted from pion-scattering data. We derive a robust bound by confronting momentum-dependent Boltzmann equations against up-to-date observations of the cosmic microwave background, of the baryonic acoustic oscillations and of primordial abundances. These datasets imply ma≤0.16 eV for the 95% credible interval, i.e., ∼30% stronger bound than what previously found. We present forecasts using dedicated likelihoods for future cosmological surveys and the sphaleron rate from unquenched lattice QCD. Published by the American Physical Society 2024

Measurement of CP Violation Observables in D+→K−K+π+ Decays

A search for violation of the charge-parity (CP) symmetry in the D+→K−K+π+ decay is presented, with proton-proton collision data corresponding to an integrated luminosity of 5.4 fb−1, collected at a center-of-mass energy of 13 TeV with the LHCb detector. A novel model-independent technique is used to compare the D+ and D− phase-space distributions, with instrumental asymmetries subtracted using the Ds+→K−K+π+ decay as a control channel. The p value for the hypothesis of CP conservation is 8.1%. The CP asymmetry observables ACP|Sϕπ+=(0.95±0.43stat±0.26syst)×10−3 and ACP|SK¯*0K+=(−0.26±0.56stat±0.18syst)×10−3 are also measured. These results show no evidence of CP violation and represent the most sensitive search performed through the phase space of a multibody decay. © 2024 CERN, for the LHCb Collaboration 2024 CERN

A method to determine the phase-space distribution of a pulsed molecular beam

Abstract We demonstrate a method to determine the longitudinal phase-space distribution of a cryogenic buffer gas cooled beam of barium-fluoride molecules based on a two-step laser excitation scheme. Temporal resolution is achieved by a transversely aligned laser beam that drives molecules from the ground state $X^2\Sigma^+$ to the $A^2\Pi_{1/2}$ state around 860\;nm, while the velocity resolution is obtained by a laser beam that is aligned counter-propagating with respect to the molecular beam and that drives the Doppler shifted $A^2\Pi_{1/2}$ to $D^2\Sigma^+$ transition around 797\;nm. Molecules in the $D$-state are detected background-free by recording the fluorescence from the $D-X$ transition at 413 nm. A temporal resolution of 11\;$\upmu$s and a velocity resolution of 6\;m/s is obtained. In order to calibrate the absolute velocity, we have determined the Doppler free transition frequencies for the $X-A$ and $X-D$ transitions with an absolute accuracy below 0.3\;MHz. The high resolution of the phase-space distributions allows us to observe a variation of the average velocity and velocity spread over the duration of the molecular beam pulse. Our method hence gives valuable insight into the dynamics in the source.

Quantum Sensitivity of a Photon-added Molecular Wave Packet

Abstract We study the temporal dynamics of a photon-added SU(2) coherent state, involving vibrational bound states of an Iodine molecule. The nonclassicality of Schrodinger cat-like and compass-like photon-added states of this anharmonic potential is explored through Mandel Q parameter and the negative region in their phase spaces. The Wigner phase space distribution is thoroughly studied for the photon added molecular state and displayed for cat- and compass-like states. Generation and control of the sub-Planck interference structures become intriguing with photon addition. We ensure that the photon addition helps to improve the quantum sensitivity for a diatomic molecular system by comparing it between photon-added and photon-subtracted states. The detailed study of quantum sensitivity reveals that, one can use a photon-added molecular wave packet as a probe to attain sensitivity to displacement, that greatly exceeds the standard quantum limit. We also report that the nature of variation of the quantum sensitivity becomes qualitatively commensurate with that of the Wigner-negativity.

Chaotic fields out of equilibrium are observable independent

Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting distribution, that rules the long-time average of every observable of interest. Before that asymptotic time scale, the statistics of chaos is generally believed to depend on both the initial conditions and the chosen observable. I show that this is not the case for a widely applicable class of models, that feature a phase-space (‘field’) distribution common to all pushed-forward or integrated observables, while the system is still relaxing towards statistical equilibrium or a stationary state. This universal profile is determined by both leading and first subleading eigenfunctions of the transport operator (Koopman or Perron–Frobenius) that maps phase-space densities forward or backward in time.

The distribution of the near-solar bound dust grains detected with Parker Solar Probe

Context. Parker Solar Probe (PSP) counts dust impacts in the near-solar region, but modeling effort is needed to understand the dust population’s properties. Aims. We aim to constrain the dust cloud’s properties based on the flux observed by PSP. Methods. We developed a forward model for the bound dust detection rates using the formalism of 6D phase space distribution of the dust. We applied the model to the location table of different PSP solar encounter groups. We explain some of the near-perihelion features observed in the data as well as the broader characteristic of the dust flux between 0.15 AU and 0.5 AU. We compare the measurements of PSP to the measurements of Solar Orbiter near 1 AU to expose the differences between the two spacecraft. Results. We found that the dust flux observed by PSP between 0.15 AU and 0.5 AU in post-perihelia can be explained by dust on bound orbits and is consistent with a broad range of orbital parameters, including dust on circular orbits. However, the dust number density as a function of the heliocentric distance and the scaling of detection efficiency with relative speed are important to explain the observed flux variation. The data suggest that the slope of differential mass distribution, δ, is between 0.14 and 0.49. The near-perihelion observations, however, show the flux maxima, which are inconsistent with the circular dust model, and additional effects may play a role. We found an indication that the sunward side of PSP is less sensitive to the dust impacts than PSP’s other surfaces. Conclusions. We show that the dust flux on PSP can be explained by noncircular bound dust and the detection capabilities of PSP. The scaling of flux with impact speed is especially important, and shallower than previously assumed.

Equilibrium dynamical models in the inner region of the Large Magellanic Cloud based on Gaia DR3 kinematics

Context. The Large Magellanic Cloud (LMC) contains complex dynamics driven by both internal and external processes. The external forces are due to tidal interactions with the Small Magellanic Cloud and the Milky Way, while internally its dynamics mainly depend on the stellar, gas, and dark matter mass distributions. Despite this complexity, simple physical models often provide valuable insights into the primary driving factors. Aims. We used Gaia Data Release 3 (DR3) to explore how well equilibrium dynamical models based on the Jeans equations and the Schwarzschild orbit superposition method are able to describe the LMC’s five-dimensional phase-space distribution and line-of-sight (LOS) velocity distribution, respectively. In the Schwarzschild model, we incorporated a triaxial bar component for the first time and derived the LMC’s bar pattern speed. Methods. We fit comprehensive Jeans dynamical models to all Gaia DR3 stars with proper motion and LOS velocity measurements found in the footprint of the VISTA near-infrared survey of the Magellanic System using a discrete maximum likelihood approach. These models are very efficient at discriminating genuine LMC member stars from Milky Way foreground stars and background galaxies. They constrain the shape, orientation, and enclosed mass of the galaxy under the assumption of axisymmetry. We used the Jeans model results as a stepping stone to more complex two-component Schwarzschild models, which include an axisymmetric disc and a co-centric triaxial bar, which we fit to the LMC Gaia DR3 LOS velocity field using a χ2 minimisation approach. Results. The Jeans models describe the rotation and velocity dispersion of the LMC disc well, and we find an inclination angle of θ = 25.5° ±0.2°, line of nodes orientation of ψ = 124° ±0.4°, and an intrinsic thickness of the disc of q0d = b/a = 0.23 ± 0.01 (minor to major axis ratio). However, bound to axisymmetry, these models fail to properly describe the kinematics in the central region of the galaxy dominated by the LMC bar. We used the derived disc orientation and the Gaia DR3 density image of the LMC to obtain the intrinsic shape of the bar. Using these two components as input to our Schwarzschild models, we performed orbit integration and weighting in a rotating reference frame fixed to the bar, deriving an independent measurement of the LMC bar pattern speed of Ω = 11 ± 4 km s−1 kpc−1. Both the Jeans and Schwarzschild models predict the same enclosed mass distribution within a radius of 6.2 kpc of ∼ 1.4 × 1010 M⊙.

Accelerating ab initio melting property calculations with machine learning: application to the high entropy alloy TaVCrW

Melting properties are critical for designing novel materials, especially for discovering high-performance, high-melting refractory materials. Experimental measurements of these properties are extremely challenging due to their high melting temperatures. Complementary theoretical predictions are, therefore, indispensable. One of the most accurate approaches for this purpose is the ab initio free-energy approach based on density functional theory (DFT). However, it generally involves expensive thermodynamic integration using ab initio molecular dynamic simulations. The high computational cost makes high-throughput calculations infeasible. Here, we propose a highly efficient DFT-based method aided by a specially designed machine learning potential. As the machine learning potential can closely reproduce the ab initio phase-space distribution, even for multi-component alloys, the costly thermodynamic integration can be fully substituted with more efficient free energy perturbation calculations. The method achieves overall savings of computational resources by 80% compared to current alternatives. We apply the method to the high-entropy alloy TaVCrW and calculate its melting properties, including the melting temperature, entropy and enthalpy of fusion, and volume change at the melting point. Additionally, the heat capacities of solid and liquid TaVCrW are calculated. The results agree reasonably with the CALPHAD extrapolated values.

Neural networks for reconstruction and uncertainty quantification of fast-ion phase-space distributions using FILD and INPA measurements

Abstract This study introduces the use of a deep convolutional neural network for reconstructing fast-ion velocity distributions from fast-ion loss detectors and imaging neutral particle analyzers (INPAs), automatically integrating uncertainty quantification through Monte Carlo dropout. The network-based reconstructions reveal pitch-angle splitting in high-energy features of lost fast-ion velocity distributions at ASDEX Upgrade during active neutral beam injection, a previously observed phenomenon now confirmed through neural networks. Moreover, contrary to common theories attributing these high-energy features to edge localized mode (ELM)-driven acceleration, we provide experimental evidence that they also occur in type-I ELM-quiescent phases. Additionally, we demonstrate improved reconstructions from INPA measurements, both synthetic and from an ASDEX Upgrade commissioning discharge, with the reconstructions closely matching TRANSP simulations. These findings suggest that neural networks can provide robust reconstructions with well-defined uncertainties, improving the reliability of interpretations of fast-ion behavior in magnetically confined plasmas.

Exploration of Halo Substructures in Integrals-of-motion Space with Gaia Data Release 3

Using kinematic data from the Gaia Data Release 3 catalog, along with metallicity estimates robustly derived from Gaia BP/RP spectra, we have explored the Galactic stellar halo in search of both known and potentially new substructures. By applying the Hierarchical Density-Based Spatial Clustering of Applications with Noise clustering algorithm in integrals-of-motion space (i.e., E, L z , and L ⊥ =Lx2+Ly2 ), we identified five previously known substructures: Gaia-Sausage-Enceladus (GSE), Helmi streams, I'itoi and Sequoia, and the hot thick disk. We additionally found NGC 3201 and NGC 5139 in this work, and NGC 3201 shares similar distributions in phase space and metallicities to Arjuna, which possibly implies that they have the same origin. Three newly discovered substructures are Prograde Substructure 1 (PG1), Prograde Substructure 2 (PG2), and the Low Energy Group. PG1, with a higher V ϕ than typical GSE member stars, is considered as either a low-eccentricity and metal-rich part of GSE or part of the metal-poor disk. PG2, sharing kinematic similarities with Aleph, is thought to be its relatively highly eccentric component or the mixture of Aleph and the disk. The Low Energy Group, whose metal-poor component of metallicity distribution function has a mean value [M/H] ∼ −1.29 (compared to that of Heracles [M/H] ∼ −1.26), may have associations with Heracles.

Erratum: Studying the squeezing effect and phase-space distribution of a single-photon-added coherent state using a postselected von Neumann measurement [Phys. Rev. A 105 , 022210 (2022)

Erratum: Studying the squeezing effect and phase-space distribution of a single-photon-added coherent state using a postselected von Neumann measurement [Phys. Rev. A <b>105</b> , 022210 (2022)

Dark matter limits from the tip of the red giant branch of globular clusters

Capture and annihilation of weakly interacting massive particle (WIMP)-like dark matter in red giant stars can lead to faster-than-expected ignition of the helium core, and thus a lower tip of the red giant branch (TRGB) luminosity. We use data to place constraints on the dark matter-nucleon cross section using 22 globular clusters with measured TRGB luminosities, and place projections on the sensitivity resulting from 161 clusters with full phase space distributions observed by . Although limits remain weaker than those from Earth-based direct detection experiments, they represent a constraint that is fully independent of dark matter properties in the solar neighborhood, probing its properties across the entire Milky Way galaxy. Based on our findings, it is likely that the use of the TRGB as a standard candle in H0 measurements is very robust against the effects of dark matter. Published by the American Physical Society 2024

First search for K+ → π0πμe decays

The first search for the lepton number violating decay K+→π0π−μ+e+ and lepton flavour violating decays K+→π0π+μ−e+, K+→π0π+μ+e− has been performed using a dataset collected by the NA62 experiment at CERN in 2016–2018. Upper limits of 2.9×10−10, 3.1×10−10 and 5.0×10−10, respectively, are obtained at 90% CL for the branching ratios of the three decays on the assumption of uniform phase-space distributions.

On the convergence of phase space distributions to microcanonical equilibrium: dynamical isometry and generalized coarse-graining

Abstract This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining procedure that leads to convergence. We prove that the time evolution of phase space distributions is an isometry for a broad class of statistical distance metrics, implying that ensembles do not get any closer to (or farther from) equilibrium, according to these metrics. This extends the known result that strong convergence of phase space distributions to the microcanonical distribution does not occur. However, it has long been known that weak convergence can occur, such that coarse-grained distributions---defined by partitioning phase space into a finite number of cells---converge pointwise to the microcanonical distribution. We define a generalization of coarse-graining that removes the need for partitioning phase space into cells. We prove that our generalized coarse-grained distribution converges pointwise to the microcanonical distribution if the dynamics are strong mixing. As an example, we study an ensemble of triangular billiard systems.

Optical Time-Domain Quantum State Tomography on a Subcycle Scale

Following recent progress in the experimental application of electro-optic sampling to the detection of the quantum fluctuations of the electromagnetic-field ground state and ultrabroadband squeezed states on a subcycle scale, we propose an approach to elevate broadband electro-optic sampling from a spectroscopic method to a full quantum tomography scheme, able to reconstruct a free-space quantum state directly in the time domain. By combining two recently developed methods to theoretically describe quantum electro-optic sampling, we analytically relate the photon-count probability distribution of the electro-optic signal to a transformed phase-space quasiprobability distribution of the sampled quantum state as a function of the time delay between the sampled midinfrared pulsed state and an ultrabroadband near-infrared probe pulse. We catalog and analyze sources of noise and show that in quantum electro-optic sampling with an ultrabroadband probe pulse one can expect to observe thermalization due to entanglement breaking. Mitigation of the thermalization noise enables a tomographic reconstruction of broadband quantum states while granting access to its dynamics on a subcycle scale. Published by the American Physical Society 2024

Evolution of the mass-radius relation of expanding very young star clusters

The initial mass–radius relation of embedded star clusters is an essential boundary condition for understanding the evolution of embedded clusters in which stars form to their release into the galactic field via an open star cluster phase. The initial mass–radius relation of embedded clusters deduced by Marks &amp; Kroupa (2012, A&amp;A, 543, A8) is significantly different from the relation suggested by Pfalzner et al. (2016, A&amp;A, 586, A68). Here, we use direct N-body simulations to model the early expansion of embedded clusters after the expulsion of their residual gas. The observationally deduced radii of clusters up to a few million years old, compiled from various sources, are well fitted by N-body models, implying that these observed very young clusters are most likely in an expanding state. We show that the mass–radius relation of Pfalzner et al. (2016) reflects the expansion of embedded clusters following the initial mass–radius relation of Marks &amp; Kroupa (2012). We also suggest that even the embedded clusters in ATLASGAL clumps with HII regions are probably already in expansion. All the clusters collected here from different observations show a mass-radius relation with a similar slope, which may indicate that all clusters were born with a profile resembling that of the Plummer phase-space distribution function.