Virial Research Articles

A new pilot wave reinterpretation for quantum AI systems

A new nonlinear Schrödinger equation is derived, which describes a cluster of bosons interacting via the strongest force. Its numerical solution points out that the cluster is stable only if the number of particles is exactly 131. The relevant kinetic and potential energies of the particles are also calculated and interrelated via the virial theorem. The developed concept is also applied to electrostatic forces.

Atomic binding corrections for high-energy fixed target experiments

High-energy beams incident on a fixed target may scatter against atomic electrons. To a first approximation, one can treat these electrons as free and at rest. For precision experiments, however, it is important to be able to estimate the size of, and when necessary calculate, subleading corrections. We discuss atomic binding corrections to relativistic lepton-electron scattering. We analyze hydrogen in detail, before generalizing our analysis to multi-electron atoms. Using the virial theorem, and many-body sum rules, we find that the corrections can be reduced to measured binding energies, and the expectation value of a single one-body operator. We comment on the phenomenological impact for neutrino flux normalization and an extraction of hadronic vacuum polarization from elastic muon electron scattering at MUonE. Published by the American Physical Society 2024

Characterizing strong-field tunneling ionization with a phase-dependent THz polarization spectrum

The terahertz radiation emitted by asymmetrically ionized wavepackets in two-color strong-field tunneling ionization is essential for detecting the system's associated electron dynamics and structural properties. We propose to characterize and control tunneling ionization using a phase-dependent terahertz polarization (PTP) spectrum, analyzed through a combination of the classical trajectory Monte Carlo method, an analytical model based on the virial theorem, and the rigorous solution of the time-dependent Schrödinger equation as a benchmark. Our results demonstrate that the PTP spectrum offers a high-precision measure of the Coulomb effect through the relative phase of the two-color laser. Comparisons of PTP results calculated using different methods suggest how the electron can be manipulated by controlling the relative phase and laser intensity. In particular, the PTP spectrum can be used to calibrate the relative phase and provides a convenient and robust reconstruction of the time-averaging of tunneling positions with high precision using the analytical model. These insights reveal that the PTP spectrum as a whole can be a new and useful tool for the all-optical characterization of ultrafast atomic and molecular ionization.

Retardation theory of eleven galaxies

Abstract The missing mass problem has been with us since the 1970s, as Newtonian gravity using baryonic mass cannot account for various observations. We investigate the viability of retardation theory, an alternative to the Dark Matter paradigm (DM) which does not seek to modify the General Principal of Relativity but to improve solutions within it by exploring its weak field approximation to solve the said problem in a galactic context. This approach have yielded satisfactory results, with respect to galactic rotation curves, the Tully-Fisher relation and missing mass derived from gravitational lensing. Recently it was able to introduce a necessary correction to the virial theorem explaining mass excess in clusters of galaxies. The current work presents eleven rotation curves calculated using Retardation Theory. The calculated rotation curves are compared with observed rotation curves. Values for the change in mass flux to mass ratio are extracted from the fitting process as a free fitting parameter. Those quantities are interpreted here and in previous works using galactic processes. Retardation Theory was able to successfully reproduce rotation curves and a preliminary correlation with star birthrate index is seen, suggesting a possible link between galactic winds and observed rotation curves. Retardation Theory shows promising results within current observations. More research is needed to elucidate the suggested mechanism and the processes which contribute to it. Galactic mass outflows carried by galactic winds may affect rotation curves.

Weighing Milky Way and Andromeda in an expanding ΛCDM Universe

The dynamics of the Local Group (LG), especially the contribution of the Milky Way (MW) and Andromeda (M 31) galaxies, is sensitive to the presence of dark energy. This work analyzes the evolution of the LG by considering it as a two-body problem in a homogeneous and isotropic expanding spacetime in a full Λcold dark matter (ΛCDM) background. Using the timing argument (TA), which links LG dynamics to LG mass, we find that the full ΛCDM background predicts a ∼10% lower mass for the LG; whereas Λ alone predicts a ∼10% higher mass. The TA mass is modified by (i) simulations and (ii) the effect of the Large Magellanic Cloud (LMC) to alleviate the poorly constrained internal mass distributions of M 31 and the MW, their time evolution, and the unknown distribution of dark matter between them. First, using IllustrisTNG simulations, we accounted for the effects of two extended halos and their environment (rather than point particles) and predicted their mass (3.89 ± 0.62)×1012 M⊙. Second, the LMC effectively changes the separation and velocities of M 31 towards the MW and reduces the predicted mass to (2.33 ± 0.72)×1012 M⊙. Despite the uncertainties around dark matter between these galaxies, the overall estimated mass is compatible with the mere sum of the MW and M 31 masses. The total mass of the TA is compatible with other estimates, such as the Hubble flow and the Virial Theorem with other dwarf galaxies. The combined result shows, for the first time, that a lower mass estimate can be obtained from the TA, with a consistent embedding and other systematic effects, and without an additional dark matter halo around the galaxies.

The virial theorem for nondifferentiable dynamical paths in resolution-scale relativity and possible implications

The virial theorem for nondifferentiable dynamical paths in resolution-scale relativity and possible implications

Virial Theorems and Equipartition of Energy for Water Waves

Virial Theorems and Equipartition of Energy for Water Waves

Revisiting the Generalised Virial Theorem and its Applications from the Perspective of Contact and Cosymplectic Geometry

Revisiting the Generalised Virial Theorem and its Applications from the Perspective of Contact and Cosymplectic Geometry

The interface of gravity and dark energy

At sufficiently large radii dark energy modifies the behavior of (a) bound orbits around a galaxy and (b) virialized gas in a cluster of galaxies. Dark energy also provides a natural cutoff to a cluster’s dark matter halo. In (a) there exists a maximum circular orbit beyond which periodic motion is no longer possible, and orbital evolution near critical binding is analytically calculable using an adiabatic invariant integral. The finding implicates the study of wide galaxy pairs. In (b), dark energy necessitates the use of a generalized Virial Theorem to describe gas at the outskirts of a cluster. When coupled to the baryonic escape condition, aided by dark energy, the results is a radius beyond which the continued establishment of a hydrostatic halo of thermalized baryons is untenable. This leads to a theoretically motivated virial radius. We use this theory to probe the structure of a cluster’s baryonic halo and apply it to X-ray and weak-lensing data collected on cluster Abell 1835. We find that gas in its outskirts deviates significantly from hydrostatic equilibrium beginning at ∼1.3 Mpc , the ‘inner’ virial radius. We also define a model dependent dark matter halo cutoff radius to A1835. The dark matter cutoff gives an upper limit to the cluster’s total mass of ∼7×1015M⊙ . Moreover, it is possible to derive an ‘outer’ hydrostatic equilibrium cutoff radius given a dark matter cutoff radius. A region of cluster gas transport and turbulence occurs between the inner and outer cutoff radii.

Statistics of Extreme Events in Integrable Turbulence.

We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schrödinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result to two fundamental scenarios of the generation of integrable turbulence: (i)the asymptotic development of the spontaneous modulational instability of a plane wave, and (ii)the long-time evolution of strongly nonlinear, partially coherent waves. In both cases, involving the bound state soliton gas dynamics, the analytically obtained values of the kurtosis are in perfect agreement with those inferred from direct numerical simulations of the fNLSE, providing the long-awaited theoretical explanation of the respective rogue wave statistics. Additionally, the evolution of a particular nonbound state gas is considered, providing important insights related to the validity of the so-called virial theorem.

Magnetic Field of Gas Giant Exoplanets and Its Influence on the Retention of Their Exomoons

We study the magnetic and tidal interactions of a gas-giant exoplanet with its host star and with its exomoons, and focus on their retention. We briefly revisit the scaling law for planetary dynamo in terms of its mass, radius, and luminosity. Based on the virial theorem, we construct an evolution law for planetary magnetic field and find that its initial entropy is important for the field evolution of a high-mass planet. We estimate the magnetic torques on orbit arising from the star–planet and planet–moon magnetic interactions, and find that it can compensate tidal torques and bypass frequency valleys where dynamical-tide response is ineffective. For exomoon’s retention, we consider two situations. In the presence of a circumplanetary disk (CPD), by comparison between CPD’s inner and outer radii, we find that planets with too strong magnetic fields or too small distance from its host star tend not to host exomoons. During the subsequent CPD-free evolution, we find, by comparison between a planet’s spin-down and a moon’s migration timescales, that hot Jupiters with periods of several days are unlikely to retain large exomoons, albeit they could be surrounded by rings from the debris of tidally disrupted moons. In contrast, moons, if formed around warm or cold Jupiters, can be preserved. Finally, we estimate the radio power and flux density due to the star–planet and planet–moon magnetic interactions and give the upper limit of detection distance by FAST.

Retarded Gravity in Disk Galaxies

Disk galaxies have a typical dimension of a few tens of kiloparsecs. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect, however, is absent in modelling used to calculate rotation curves throughout entire galaxies and their external gas. The considerable differences between Newtonian predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that by applying general relativity in a rigorous fashion, without neglecting retardation, one can explain the rotational velocities of galactic matter without modifying gravity or adding dark matter. Moreover, it was shown that dark matter effects, as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. It must be noted, however, that the proposed theory relies on the existence of a mass flow (of a changing rate) into the galaxy; a requirement that was not directly observed. In the original paper on the subject only one galaxy (M33) was analysed in detail. This was later amended with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain very accurate fits to the data.

Deterministic engines extending Helmholtz thermodynamics

Helmholtz formalism provides a tantalizing interpretation of classical thermodynamics, based on time integrals of purely mechanical quantities and without need of statistical description. Here we extend this approach to include heat flux and pressure at the walls to enable it to describe actual thermodynamic transformations, such as isothermal compressions and expansions. The presence of hard walls, which gives rise to non zero pressure, is justified by means of the virial theorem, while the heat fluxes are introduced as quasi-static limits of suitably thermostatted Hamiltonians. Particular attention is paid to generalizing the minimalist cases of the harmonic oscillator and elastic bouncer, which afford clear physical interpretations. With such extensions, a complete picture of thermodynamics emerges, amenable to phase transitions and cyclic deterministic transformations, which produce mechanical work from heat, like the Carnot cycle.

Total and dark mass from observations of galaxy centers with machine learning

The galaxy total mass inside the effective radius is a proxy of the galaxy dark matter content and the star formation efficiency. As such, it encodes important information on the dark matter and baryonic physics. Total central masses can be inferred via galaxy dynamics or gravitational lensing, but these methods have limitations. We propose a novel approach based on machine learning to make predictions on total and dark matter content using simple observables from imaging and spectroscopic surveys. We used catalogs of multiband photometry, sizes, stellar mass, kinematic measurements (features), and dark matter (targets) of simulated galaxies from the Illustris-TNG100 hydrodynamical simulation to train a Mass Estimate machine Learning Algorithm ( Mela ) based on random forests. We separated the simulated sample into passive early-type galaxies (ETGs), both normal and dwarf, and active late-type galaxies (LTGs) and showed that the mass estimator can accurately predict the galaxy dark masses inside the effective radius in all samples. We finally tested the mass estimator against the central mass estimates of a series of low-redshift (zlsim 0.1) datasets, including SPIDER, MaNGA/DynPop, and SAMI dwarf galaxies, derived with standard dynamical methods based on the Jeans equations. We find that Mela predictions are fully consistent with the total dynamical mass of the real samples of ETGs, LTGs, and dwarf galaxies. learns from hydro-simulations how to predict the dark and total mass content of galaxies, provided that the real galaxy samples overlap with the training sample or show similar scaling relations in the feature and target parameter space. In this case, dynamical masses are reproduced within 0.30 dex ($ with a limited fraction of outliers and almost no bias. This is independent of the sophistication of the kinematical data collected (fiber vs. 3D spectroscopy) and the dynamical analysis adopted (radial vs. axisymmetric Jeans equations, virial theorem). This makes a powerful alternative to predict the mass of galaxies of massive stage IV survey datasets using basic data, such as aperture photometry, stellar masses, fiber spectroscopy, and sizes. We finally discuss how to generalize these results to account for the variance of cosmological parameters and baryon physics using a more extensive variety of simulations and the further option of reverse engineering this approach and using model-free dark matter measurements (e.g., via strong lensing), plus visual observables, to predict the cosmology and the galaxy formation model.

Virial Theorem of Clausius

Virial Theorem of Clausius

Active galactic nuclei and gravitational redshifts

Gravitational redshift is a classical effect of General Relativity. It has been measured in stars, quasars, and clusters of galaxies. We identify the signature of gravitational redshift in the emission lines of active galaxies that is caused by supermassive black holes and compare this signature to what is found for inactive galaxies. Using the virial theorem, we estimated gravitational redshifts for quasars from the 14th data release (DR14) of the Sloan Digital Sky Survey (SDSS) and compared them with measured gravitational redshifts from the difference between the redshifts of emission lines of Sydney Australian Astronomical Observatory Multi-object Integral Field (SAMI) galaxies in the central and outer annuli of their integral field spectra. Firstly, from the full width at half maximum of $H_ beta$ lines of 57 Seyfert type I galaxies of the active galactic nucleus (AGN) Black Hole Mass Database, we derive a median gravitational redshift $z_g = 1.18 $. Expanding this analysis to 86755 quasars from DR14 of SDSS, we have a median value $z_g = 1.52 . Then, by comparing the redshifts of lines measured in the central and outer regions of low-ionization nuclear emission-line region galaxies in the SAMI survey, we obtain $z_g = (0.68 which increases to $z_g = (1.0 $ for the $H_ and $H_ lines . These numbers are compatible with central black holes of $ 10^9$ solar masses and broad line regions of $ 1$ pc. For non-AGN galaxies, the gravitational redshift is compatible with zero.

On the notion of strong correlation in electronic structure theory.

Strong correlation has been said to have many faces, and appears to have many synonyms of questionable suitability. In this work we aim not to define the term once and for all, but to highlight one possibility that is both rigorously defined and physically transparent, and remains so in reference to molecules and quantum lattice models. We survey both molecular examples - hydrogen systems (Hn, n = 2, 4, 6), Be2, H-He-H, and benzene - and the half-filled Hubbard model over a range of correlation regimes. Various quantities are examined including the extent of spin symmetry breaking in correlated single-reference wave functions, energetic ratios inspired by the Hubbard model and the Virial theorem, and metrics derived from the one- and two-electron reduced density matrices (RDMs). The trace and the square norm of the cumulant of the two-electron reduced density matrix capture what may well be defined as strong correlation. Accordingly, strong correlation is understood as a statistical dependence between two electrons, and is distinct from the concepts of "correlation energy" and more general than entanglement quantities that require a partitioning of a quantum system into distinguishable subspaces. This work enables us to build a bridge between a rigorous and quantifiable regime of strong electron correlation and more familiar chemical concepts such as anti-aromaticity in the context of Baird's rule.

Quantum fundaments of catalysis: true electronic potential energy.

Catalysis is a quantum phenomenon enthalpically driven by electronic correlations with many-particle effects in all of its branches, including electro-photo-catalysis and electron transfer. This means that only probability amplitudes provide a complete relationship between the state of catalysis and observations. Thus, in any atomic system material), competing space-time electronic interactions coexist to define its (related) properties such as stability, (super)conductivity, magnetism (spin-orbital ordering), chemisorption and catalysis. Catalysts, reactants, and chemisorbed and transition states have the possibility of optimizing quantum correlations to improve reaction kinetics. Active sites with closed-shell orbital configurations share a maximum number of spin-paired electrons, mainly optimizing coulombic attractions and covalency and defining weakly correlated closed-shell (WCCS) structures. However, in compositions with open-shell orbital configurations, at least, quantum spin exchange interactions (QSEIopenshells) arise, stabilising unpaired electrons in less covalent bonds and differentiating non-weakly (or strongly) correlated open-shell (NWCOS) systems. In NWCOS catalysts, electronic ground states can have bonds with diverse and rival spin-orbital orderings as well as ferro-, ferri- and multiple antiferro-magnetic textures, which deeply define their activities. Particularly in inter-atomic ferromagnetic (FM) bonds, the increase in relevance of non-classical quantum potentials can significantly optimize chemisorption energies, transition states (TSs), activation energies (overpotential) and spin-dependent electron transfer (conductivity), overall implying the need for explaining the thermodynamic and kinetic origin of catalysis from its true quantum electronic energy. To do so, we use the connection between the Born-Oppenheimer approximation and Virial theorem in the treatment of electronic kinetic and potential energies. Thus, the exact fundamental interactions that decompose TSs appear. The possibility of increasing the stabilization of TSs, due to quantum correlations on NWCO catalysts, opens the possibility of simultaneously reducing chemisorption enthalpies and activation barriers of reaction mechanisms, which implies the anticipation and explanation of positive deviations from the Brønsted-Evans-Polanyi principle.

Constraining the Milky Way Dynamic Mass and Newtonian Gravity through the Proper Motion of Messier’s Globular Clusters

The estimation of the proper motion of globular clusters is presented from the oldest observations of Messier's Globular clusters, comparing with NASA-NED and GAIA. The period-distance relationship, without assuming Dark matter models, allows us to limit the dynamic mass of the Milky Way and the invalidity of the Keplerian movement of Globular Clusters. The best fitting data are 14 2.3 0.3210 ± M for the dynamical mass, and β ≅ −5 3 in agreement with the generalization of the Virial Theorem in large-scale modified Newtonian gravity models.

Eigensolutions, virial theorem and molecular study of nonrelativistic Krazer‐Fues potential

AbstractA Kratzer‐Fues potential is coupled with its self to form a double Kratzer‐Fues potential. The solutions of the radial Schrödinger equation with the combined potential are obtained via two different methodologies. Using the supersymmetric approach, the energy equation for a non‐approximated centrifugal term is obtained. The energy equation for the approximated centrifugal term is obtained using the parametric Nikiforov‐Uvarov method. Numerical results are computed for five molecules using MATLAB software program. The computed numerical values are compared with the experimental values and the ground state energy obtained from Herzberg's energy level equation. The study revealed that the results of the approximated centrifugal term are better than the results of the non‐approximated centrifugal term for four molecules.