Finite Mass Research Articles

Impacts of Generalized Uncertainty Principle on the Black Hole Thermodynamics and Phase Transition in a Cavity

In this work, we conduct a study regarding the thermodynamic evolution and the phase transition of a black hole in a finite spherical cavity subject to the generalized uncertainty principle. The results demonstrate that both the positive and negative generalized uncertainty principle parameters β0 can significantly affect the thermodynamic quantities, stability, critical behavior, and phase transition of the black hole. For β0 > 0, the black hole forms a remnant with finite temperature, finite mass, and zero local heat capacity in the last stages of evolution, which can be regarded as an elementary particle. Meanwhile, it undergoes one second-order phase transition and two Hawking-Page-type phase transitions. The Gross-Perry-Yaffe phase transition occurs for both large black hole configuration and small black hole configuration. For β0 < 0, the Gross-Perry-Yaffe phase transition occurs only for large black hole configuration, and the temperature and heat capacity of the black hole remnant is finite, whereas its mass is zero. This indicates the remnant is metastable and would be in the Hawking-Page-type phase transition forever. Specifically, according to the viewpoint of corpuscular gravity, the remnant can be interpreted as an additional metastable tiny black hole configuration, which never appears in the original case and the positive correction case.

Observation of Massless and Massive Collective Excitations with Faraday Patterns in a Two-Component Superfluid.

We report on the experimental measurement of the dispersion relation of the density and spin collective excitation modes in an elongated two-component superfluid of ultracold bosonic atoms. Our parametric spectroscopic technique is based on the external modulation of the transverse confinement frequency, leading to the formation of density and spin Faraday waves. We show that the application of a coherent coupling between the two components reduces the phase symmetry and gives a finite mass to the spin modes.

Field-Theoretical Representation of Interactions between Particles: Classical Relativistic Probability-Free Kinetic Theory

It was proven that the class of stable interatomic potentials can be represented exactly as a superposition of Yukawa potentials. In this paper, an auxiliary scalar field was introduced to describe the dynamics of a system of neutral particles (atoms) in the framework of classical field theory. In the case of atoms at rest, this field is equivalent to the interatomic potential, but in the dynamic case, it describes the dynamics of a system of atoms interacting through a relativistic classical field. A relativistic Lagrangian is proposed for a system consisting of atoms and an auxiliary scalar field. A complete system of equations for the relativistic dynamics of a system consisting of atoms and an auxiliary field was obtained. A closed kinetic equation was derived for the probability-free microscopic distribution function of atoms. It was shown that the finite mass of the auxiliary field leads to a significant increase in the effect of interaction retardation in the dynamics of a system of interacting particles.

Benchmark calculations of the 3 D Rydberg spectrum of beryllium

High-accuracy calculations are performed for the four lowest states of the beryllium atom. All-electron explicitly correlated Gaussian (ECG) functions are employed to expand the functions and the non-relativistic internal Hamiltonian used in the calculations, which is obtained by rigorously separating out the centre-of-mass motion from the laboratory-frame Hamiltonian, explicitly depends on the finite nuclear mass of Be. The nonrelativistic wave functions of the considered states of Be are generated variationally with the nonlinear parameters of the Gaussians optimised using a procedure that employs the energy gradient determined with respect to these parameters. The nonrelativistic wave functions are used to calculate the leading relativistic corrections employing the perturbation theory at the first-order level. Only corrections that do not produce fine/hyperfine splitting of the energy levels are considered. The corrections are added to the nonrelativistic energies and the results are used to calculate the so-called ‘centre of gravity’ transition energies with respect to the Be ground state. A comparison with high-quality experimental results shows agreement to within about 0.6 cm.

Emergence of many-body quantum chaos via spontaneous breaking of unitarity

It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as $K(\ensuremath{\eta},t)=\ensuremath{\langle}|\mathrm{Tr}exp(\ensuremath{-}\ensuremath{\eta}H+itH){|}^{2}\ensuremath{\rangle}$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the ``unitary'' $\ensuremath{\eta}=0$ case is different from the $\ensuremath{\eta}\ensuremath{\rightarrow}{0}^{\ifmmode\pm\else\textpm\fi{}}$ limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp in the SFF, which is responsible for the fast emergence of Poisson statistics in the noninteracting case, and gives rise to a nontrivial random matrix structure of many-body levels. The interaction-induced mass in the SFF shares similarities with the dephasing rate in the theory of weak localization and the Lyapunov exponent of the out-of-time-ordered correlators.

Time dependent nature of the Neptune’s arc configuration

By distinguishing the main arc Fraternite from the minor arcs Egalite (2,1), Liberte, Courage, the conservative restricted three-body system is extended to a non-conservative restricted four-body system with the central body Neptune S, the primary body Galatea X, a minor body Fraternite F, and a test body s. Through the equations of motion, it is shown that the locations where the force is null (null points) along the orbit of s correspond to the locations of Egalite (2,1), Liberte, and Courage. Even if all the arcs were captured by three-body CER sites initially, the orbits over the CER potential maxima would be unstable for the minor arcs due to the disturbing force of Fraternite with finite mass, allowing them to be relocated to the four-body null points. On the other hand, the minor arcs do not have the mass to destabilize Fraternite from its three-body CER site, which is enlarged from 8.37 degrees to 9.7 degrees thus accounting for the Fraternite’s span. In this non-conservative restricted four-body system, s is under the effects of the potentials of X and F, therefore the null points are not absolutely stable as the Lagrangian points. The potential of X drives a long period harmonic pendulum oscillation through Φ s x = [ ( n + 1 ) θ s − n θ x − ϕ s ] centered over a four-body null point with T = 1 , 000 d , while the potential of F drives a much longer period singular pendulum oscillation through Δ θ s f centered over Fraternite with T f = 40 , 000 d . In this four-body system, the dynamics of these two oscillations generates a time alternating symmetric arc configuration about Fraternite with a century long time scale. The non-conservative nature of this system could account for the time varying intensity, configuration, and disappearance of the minor arcs.

Is natural convection within an aquifer a critical phenomenon in deep borehole heat exchangers' efficiency?

Deep borehole heat exchangers (BHEs) can be utilised effectively for geothermal (heat) extraction from up to a few kilometres below the subsurface using the conventional closed U-loop or coaxial configurations. These systems take advantage of the high enthalpy energy in the deeper ground without relying on fracture flow extraction/injection, hence avoiding the complexity and uncertainty of hydraulic fracturing to enhance the permeability of deep aquifers. Despite the recent theoretical advancement in deep BHE systems, recent studies mainly assume conductive heat transfer in the ground, neglecting the effects of groundwater and heat convection (natural or forced) on the system’s thermal capacity. This simplified assumption could result in underestimating geothermal extraction efficiency given the extensive fluctuations in groundwater thermo-physical properties, particularly at high temperatures. Therefore, the ultimate goal of this study is to investigate the extent to which the thermal performance of deep coaxial borehole heat exchangers (CBHEs) is affected by natural convection in deep aquifers. This is achieved by developing a novel numerical approach for reliable quantification of thermal yield, accounting for conduction and the commonly overlooked thermo-induced convection in aquifers - using a tested 3D finite element heat and mass transport model. Considering groundwater parameters’ temperature dependency, the resultant buoyancy in groundwater and the effects of gravity, parametric studies are undertaken for various ranges of permeability, carrier fluid velocity and CBHEs depth. The overall validity of the model is tested against published experimental data. It is concluded that higher carrier fluid inflow rates for a given CBHE depth can lead to up to 43% higher CBHEs thermal efficiency when the aquifer’s permeability is high (k = 10−10 m2). Furthermore, the results indicate that a higher aquifer permeability, hence a substantial thermo-induced heat exchange in the aquifer, has a more pronounced effect on CBHEs thermal yield than carrier fluid inflow rate in shorter CBHEs (63% vs 17% increase), which contradicts the behaviour of longer CBHEs in which the thermo-induced convective heat transfer in aquifers with higher permeability, i.e., k = 10−10 m2 and carrier fluid inflow rate could have a similar effect on the system’s efficiency (45% vs 43% increase). In general, it is concluded that an accurate evaluation of how system parameters such as the inflow rate and CBHE’s depth could contribute to CBHE’s thermal yield requires a good understanding of the impacts of aquifer’s characteristics, i.e., temperatures, permeability and depth on thermo-induced heat exchange in the aquifer, which is facilitated using the proposed numerical model.

W + charm production with massive c quarks in PowHel

The hadroproduction of a W boson in association with a charm quark at the Large Hadron Collider is at the centre of current investigations due to its potential to probe the strangeness content of the proton. In this paper we present an implementation of the W + c production process in the PowHel event generator matched to the PYTHIA8 parton shower approach, allowing to obtain predictions for differential cross-sections with NLO QCD accuracy matched to the accuracy of the Shower Monte Carlo event generator. Effects of non-diagonal CKM matrix elements, finite charm quark mass and off-shell W decays including spin correlations are taken into account. We investigate the production of a leptonically decaying W boson in association with either a charmed meson (W± + D∗∓) or a charmed jet (W± + jc) and compare our predictions with particle-level measurements by the ATLAS and CMS collaborations at sqrt{s} = 7 and 13 TeV. The role of the so-called “opposite sign” and “same sign” contributions to the theoretical cross-sections is presented and discussed, pointing out the importance of including parton shower effects for a reliable estimate of the latter and a faithful comparison with experimental data.

Quasi-one-dimensional graphene structure: Study of finite bandgap and effective mass with width

Quasi-one-dimensional graphene structure: Study of finite bandgap and effective mass with width

One loop mechanism for neutrinoless double beta hyperon decay

Motivated by the large dataset to be accumulated of hyperon pairs produced in decays of $\mathcal{O}(10^{10})$ $J/\psi$ and $\psi^\prime$ charmonia states in the BES-III collaboration, we revisited the predictions of $\Delta L=2$ decays of hyperons $B^-_i\to B^+_f\ell^-\ell'^-$ in the one-loop model mechanism involving Majorana neutrinos previously presented in \cite{Barbero:2002wm}. Unlike the previous work, by modeling the momentum transfer dependence of the hyperon form factors in the computation we provide finite results for the loop integration. Furthermore, since we keep finite masses for the neutrinos throughout the calculations, we are able to consider the effects of heavy Majorana neutrinos. Thus, our results are applied to a simple model that involves two Majorana heavy neutrinos in the framework of a low-scale seesaw model. In order to provide and compare additional predictions, we study an alternative model where $\Delta L=2$ decays are induced by the short-range effects of a scalar boson coupled to di-leptons.

Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows

For the three dimensional axisymmetric Euler flow, we construct a family of solutions with multiple travelling vortex rings, with large speed of order O(|lnɛ|), where ɛ>0 is a small parameter. Our construction is based on the analysis of the following nonlinear elliptic equation: ∂rrψ+3r∂rψ+∂zzψ=−F((ψ−α2|lnɛ|)r2),(r,z)∈R2,ψr(0,z)=0forr=0,for some special functions F, where α is a parameter. The location of the vortex rings is governed by some balancing systems, which can be solved by the polynomial method in several special cases. For the non-swirl case, in the core of each vortex ring, our solutions can be regarded as a rescaled finite mass solution of the Liouville equation. The results can be generalized directly to the case with swirl, for which we also construct different types of solutions with multiple vortex rings.

Power-Optimal Control of a Stirling Engine's Frictional Piston Motion.

The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular mechanical friction. We use a low-effort endoreversible Stirling engine model, which allows for the incorporation of finite heat and mass transfer as well as the friction caused by the piston motion. Instead of performing a parameterization of the piston motion and optimizing these parameters, we here use an indirect iterative gradient method that is based on Pontryagin’s maximum principle. For the varying friction coefficient, the optimization results are compared to both, a harmonic piston motion and optimization results found in a previous study, where a parameterized piston motion had been used. Thus we show how much performance can be improved by using the more sophisticated and numerically more expensive iterative gradient method.

Near-exact non-relativistic ionization energies for many-electron atoms.

Electron–electron interactions and correlations form the basis of difficulties encountered in the theoretical solution of problems dealing with multi-electron systems. Accurate treatment of the electron–electron problem is likely to unravel some nice physical properties of matter embedded in the interaction. In an effort to tackle this many-body problem, a symmetry-dependent all-electron potential generalized for an n-electron atom is suggested in this study. The symmetry dependence in the proposed potential hinges on an empirically determined angular momentum-dependent partitioning fraction for the electron–electron interaction. With the potential, all atoms are treated in the same way regardless of whether they are open or closed shell using their system specific information. The non-relativistic ground-state ionization potentials for atoms with up to 103 electrons generated using the all-electron potential are in reasonable agreement with the existing experimental and theoretical data. The effects of higher-order non-relativistic interactions as well as the finite nuclear mass of the atoms are also analysed.

Особенности применения комбинированного функционала масса — время при решении задачи оптимизации многовиткового выведения космического аппарата на высокоэнергетическую орбиту

Through the example of a non-coplanar transfer of an orbital unit with a low reference to a geostationary orbit, the paper describes the main aspects of applying the combined mass–time functional to the problem of optimizing multiple-burn transfer using the maximum principle. The study analyzes the saturation of the dependence of the orbital unit’s mass in the target orbit on the weight coefficient for a wide range of the orbital unit’s mass-energy characteristics of upper stages for a given structure of the optimal trajectory. Furthermore, a similar analysis was carried out for structures of optimal trajectories containing a different number of perigee active sections, with fixed mass-energy characteristics of the upper stage. The ranges of variation of the weight coefficient are demonstrated, in which there are optimal schemes containing a different number of perigee active sites. Recommendations are given for setting the saturation coefficient, at which the solution of the problem with the combined functional can be considered coinciding with the solution of the problem of maximizing the finite mass of the orbital block.

Diamagnetic susceptibility from a nonadiabatic path-integral simulation of few-electron systems

Diamagnetism is the response of dynamical compositions of charged particles, electrons, and nuclei, to an incident magnetic field. In this paper, we study how the finite temperature and finite nuclear masses affect the diamagnetic susceptibilities of selected small atoms and molecules, as limiting cases of dilute gas. We use nonrelativistic path-integral Monte Carlo simulation (PIMC), where both electrons and nuclei are treated on equal footing at finite temperatures in sampling exact Coulomb pair density matrices. The PIMC estimator of diamagnetic susceptibility has been briefly introduced in Ceperley [D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995)], but here we present a comprehensive derivation, discussion of practical effects, and proof-of-concept results for selected few-body Coulomb systems. Our results are in perfect agreement with high-accuracy literature references, where available, but also demonstrate additional thermal effects of the diamagnetic response of low-mass systems.

Path integral for quantum Mabuchi K-energy

We construct a measure (of finite total mass) on the space of metrics of a fixed 1-dimensional complex manifold (of genus greater than or equal to 2) which corresponds in the physics literature to a path integral based on a Gibbs type measure with energy given by the sum of the Liouville action and the Mabuchi K-energy. To the best of our knowledge, this is the first rigorous construction of such an object and this is done by means of probabilistic tools. Both functionals (the Liouville functional and the K-energy functional) play an important role, respectively, in Riemannian geometry (in the case of surfaces) and Kähler geometry. As an output, we obtain a measure whose Weyl anomaly displays the standard Liouville anomaly plus an additional K-energy. Motivations come from theoretical physics where these type of path integrals arise as models for fluctuating metrics on surfaces when coupling certain nonconformal matter fields (mathematically noncritical statistical physics models) to quantum gravity as advocated by A. Bilal, F. Ferrari, S. Klevtsov, and S. Zelditch. On the discrete side, our measure is expected to describe the scaling limit of large planar maps decorated by some noncritical statistical physics models. Interestingly, our computations show that quantum corrections perturb the classical Mabuchi K-energy and produce a quantum Mabuchi K-energy: these type of corrections are reminiscent of the quantum Liouville theory. Our probabilistic construction relies on a variant of the theory of Gaussian multiplicative chaos (GMC) and derivative GMC (DGMC for short). The technical backbone of our construction consists in two estimates on (derivative and standard) GMC which are of independent interest in probability theory. First, we show that these DGMC random variables possess negative exponential moments, and second, we derive optimal small deviations estimates for the GMC associated to a recentered Gaussian free field (GFF).

Abinitio determination of the polarizability of neon

The static electric-dipole polarizability $\ensuremath{\alpha}$ of the neon atom was determined with a relative uncertainty of only about 0.003% using state-of-the-art ab initio approaches. The new value, $\ensuremath{\alpha}=2.661\phantom{\rule{0.16em}{0ex}}067(77)\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$, is almost five times more accurate than the previous ab initio estimate, $\ensuremath{\alpha}=2.660\phantom{\rule{0.16em}{0ex}}80(36)\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$, by Lesiuk et al. [Phys. Rev. A 102, 052816 (2020)]. Similar to their work, we calculated $\ensuremath{\alpha}$ using ab initio methods up to full configuration interaction and added corrections for finite nuclear mass and size, relativistic, and quantum electrodynamics (QED) effects. The uncertainty reduction of this work was achieved in particular by employing extremely large basis sets, including newly developed ones of 11Z, 12Z, and 13Z quality. Moreover, the finite nuclear mass effects and most of the relativistic contributions were calculated at much higher levels of theory than in the work of Lesiuk et al. However, we adopted their values for the orbit-orbit part of the relativistic correction and for the Bethe logarithm needed to compute the QED correction. The uncertainty of our final value is still an order of magnitude larger than that of the experimental value recently measured by Gaiser and Fellmuth [Phys. Rev. Lett. 120, 123203 (2018)] with an uncertainty of only a few parts per million using dielectric-constant gas thermometry. Yet, our ab initio value agrees with their value, ${\ensuremath{\alpha}}_{\mathrm{exp}}=2.661\phantom{\rule{0.16em}{0ex}}057(7)\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$, almost within the experimental uncertainty. This could indicate that the higher-order relativistic corrections and QED contributions, which dominate our uncertainty budget, are more accurate than expected considering the uncontrolled approximations involved in their calculation.

Vanishing viscosity limit of the three-dimensional barotropic compressible Navier–Stokes equations with degenerate viscosities and far-field vacuum

We are concerned with the inviscid limit of the Navier–Stokes equations to the Euler equations for barotropic compressible fluids in \mathbb{R}^3 . When the viscosity coefficients obey a lower power law of the density (i.e., \rho^\delta with 0<\delta<1 ), we identify a quasi-symmetric hyperbolic–singular elliptic coupled structure of the Navier–Stokes equations to control the behavior of the velocity of the fluids near a vacuum. Then this structure is employed to prove that there exists a unique regular solution to the corresponding Cauchy problem with arbitrarily large initial data and far-field vacuum, whose life span is uniformly positive in the vanishing viscosity limit. Some uniform estimates on both the local sound speed and the velocity in H^3(\mathbb{R}^3) with respect to the viscosity coefficients are also obtained, which lead to the strong convergence of the regular solutions of the Navier–Stokes equations with finite mass and energy to the corresponding regular solutions of the Euler equations in L^{\infty}([0, T]; H^{s}_{\mathrm{loc}}(\mathbb{R}^3)) for any s\in [2, 3) . As a consequence, we show that, for both viscous and inviscid flows, it is impossible that the L^\infty norm of any global regular solution with vacuum decays to zero asymptotically, as t tends to infinity. Our framework developed here is applicable to the same problem for other physical dimensions via some minor modifications.

Regularity estimates for singular parabolic measure data problems with sharp growth

We prove global gradient estimates for parabolic p-Laplace type equations with measure data, whose model isut−div(|Du|p−2Du)=μinΩ×(0,T)⊂Rn×R,where μ is a signed Radon measure with finite total mass. We consider the singular case2nn+1<p≤2−1n+1and give possibly minimal conditions on the nonlinearity and the boundary of Ω, which guarantee the regularity results for such measure data problems.

Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data

In this paper, we consider the Cauchy problem to the planar non-resistive magnetohydrodynamic equations without heat conductivity, and establish the global well-posedness of strong solutions with large initial data. The key ingredient of the proof is to establish the a priori estimates on the effective viscous flux and a newly introduced “transverse effective viscous flux” vector field inducted by the transverse magnetic field. The initial density is assumed only to be uniformly bounded and of finite mass and, in particular, the vacuum and discontinuities of the density are allowed.