Infinite Mass Research Articles

Dean–Kawasaki equation with initial condition in the space of positive distributions

We show that the Dean–Kawasaki equation does not admit non-trivial solutions in the space of tempered measures. More specifically, we consider martingale solutions taking values, and with initial conditions, in the subspace of measures admitting infinite mass and satisfying some integrability conditions. Following work by the first author, Lehmann and von Renesse (Electron Commun Probab 24:3916340, 2019), we show that the equation only admits solutions if the initial measure is a discrete measure. Our result extends the previously mentioned works by allowing measures with infinite mass.

Kink-antikink collisions in hyper-massive models

We study topological kinks and their interactions in a family of scalar field models with a double well potential parametrized by the mass of small perturbations around the vacua, ranging from the mass of the ϕ4 Klein-Gordon model all the way to the limit of infinite mass, which is identified with a non-analytic potential. In particular, we look at the problem of kink-antikink collisions and analyze the windows of capture and escape of the soliton pair as a function of collision velocity and model mass. We observe a disappearance of the capture cases for intermediary masses between the ϕ4 and non-analytic cases. The main features of the kink-antikink scattering are reproduced in a collective coordinates model, including the disappearance of the capture cases.

Evolution of creases on the event horizon of a black hole merger

A generic black hole merger occurs through a restructuring of creases (sharp edges) on the event horizon. This process is studied for a black hole merger in the limit of infinite mass ratio, for which constructing the event horizon reduces to finding a null hypersurface that asymptotes to a Rindler horizon in the Kerr spacetime. Geometrical properties of the creases on this horizon are determined and the results are compared with the predictions of an exact local description of the event horizon in a generic merger. The crease set is shown to have finite area. A recently proposed expression for the gravitational entropy of a crease is shown to diverge at the instant of merger. Caustics on (and off) the event horizon are determined by exploiting the correspondence with the problem of gravitational lensing by a Kerr black hole. Caustics form an “astroid tube” in spacetime, two edges of which lie on the event horizon of the merger. Perturbative expressions for the location of this tube are presented, extending previous work to much higher perturbative order. Published by the American Physical Society 2024

Defect induced heavy meson dynamics in the QCD conformal window

Upon introducing a heavy quark in the perturbative regime of the QCD conformal window we precisely determine the associated heavy meson spectrum and wave functions in terms of the number of light flavors and mass. We then compute the conformal Isgur-Wise function which is a central quantity in heavy quark physics. We further determine the impact of the residual low energy confining dynamics on the heavy meson spectrum. As a working framework, we adapt the heavy quark effective theory to the perturbative conformal window dynamics. Our work lays the foundations to systematically go beyond the infinite mass defect approximation in conformal field theories. Published by the American Physical Society 2024

Some asymptotic profiles for the viscous Burgers equation with infinite mass

Some asymptotic profiles for the viscous Burgers equation with infinite mass

The very singular solution for the Anisotropic Fast Diffusion Equation and its consequences

We construct the Very Singular Solution (VSS) for the Anisotropic Fast Diffusion Equation (AFDE) in the suitably good exponent range. VSS is a solution that, starting from an infinite mass located at one point as initial datum, evolves as an admissible solution of the corresponding equation everywhere away from the point singularity. It is expected to represent important properties of the fundamental solutions when the initial mass is very big. Here we work in the whole Euclidean space.In this setting we show how the diffusion process distributes mass from the initial infinite singularity with different rates along the different space directions. Indeed, and up to constant factors, there is a simple partition formula for the anisotropic mass expansion, given approximately as the minimum of separate 1-D VSS solutions. This striking fact is a consequence of the improved scaling properties of the special solution, and it has strong consequences.If we consider the family of fundamental solutions for different masses, we prove that they all share the same universal tail behaviour (i.e., for large |x|) as the VSS. Namely, their tail is asymptotically convergent to the unique VSS tail. This means that the VSS partition formula holds also for the fundamental solutions at spatial infinity. With the help of this analysis we study the behaviour of the class of nonnegative finite-mass solutions of the Anisotropic FDE, and prove the Global Harnack Principle (GHP) and the Asymptotic Convergence in Relative Error (ACRE) under a natural assumption on the decay of the initial tail.

Boosting energy levels in graphene magnetic quantum dots through magnetic flux and inhomogeneous gap

We study the effects of a magnetic flux and an inhomogeneous gap on the energy spectrum of graphene magnetic quantum dots (GMQDs). By considering the Dirac equation in the infinite mass framework, we can analytically obtain eigenspinor expressions. By applying boundary conditions, we obtain an energy spectrum equation in terms of system parameters such as radius, magnetic field, energy, flux, and gap. In the infinite limit, we recover Landau levels for graphene in a magnetic field. We show that the energy spectrum increases significantly in the presence of flux and a gap inside the GMQDs, which prolongs the lifetime of the trapped electron states. We show that higher flux also produces new Landau levels of negative angular momentum. Meanwhile, we find that the gap increases the separation between the electron and hole energy bands. As shown in the radial probability analysis, flux and gap emerge as influential factors in controlling electron mobility, affecting confinement, and prolonging the presence of quasi-bound states.

Nonlinear enhanced dissipation in viscous Burgers-type equations

We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than the solution of the heat equation for the same initial data in this class. In other words, we show an enhanced dissipation coming from a nonlinear transport term. We compute the asymptotic profile in this class for both equations. For the viscous Burgers equation, the main novelty is the construction and description of a time-dependent profile with a boundary layer, which enhances the dissipation. This profile will be stable up to a computable nonlinear correction depending on the perturbation. We also extend our results to other convection–diffusion equations.

Shock waves at final stages of cavity collapse in non-homogeneous liquid with divergenceless flow

We show the emergence of shock waves at the final stages of the complete collapse of a spherical cavity in a liquid with a smoothly decreasing density. The well-known Rayleigh assumption of fluid homogeneity is altered, while maintaining that of divergenceless flow. The fundamental difference between both infinite liquids is that his has an infinite mass, while ours, a finite one. Given the ease of deformation of non-homogeneous media in relation to homogeneous ones, as observed in several materials, all Rayleigh results are modified, including the cavity wall speed and acceleration, total time of complete collapse, and distribution of pressure in the infinite liquid. Rather than the homogeneous Rayleigh fluid, our non-homogeneous liquid can support a finite local sound speed. As a result, we succeed to show the emergence of shock patterns at the final stages of the cavity collapse. The analytical formulation is compared with underwater implosion and explosion experiments and simulations. Possible applications as a benchmark test for hydrocodes are briefly discussed.

Ground-state energy of H−: a critical test of triple basis sets

We report an improved variational upper bound for the ground state energy of H− using Hylleraas-like wave functions in the form of a triple basis set having three distinct distance scales. The extended precision DQFUN of Bailey, allowing for 70 decimal digit arithmetic, is implemented to retain sufficient precision. Our result exceeds the previous record [A. M. Frolov, Euro. J. Phys. D 69, 132 (2015)], indicating that the Hylleraas triple basis set exhibits comparable convergence to the widely used pseudorandom all-exponential basis sets, but the numerical stability against roundoff error is much better. It is argued that the three distance scales have a clear physical interpretation. The new variational bound for infinite nuclear mass is –0.527 751 016 544 377 196 590 814 478 a.u. New variational bounds are also presented for the finite mass cases of the hydrogen, deuterium, and tritium negative ions H−, D−, and T−.

Ultrafast field-driven valley polarization of transition metal dichalcogenide quantum dots

We study theoretically the electron dynamics of transition metal dichalcogenide (TMDC) quantum dots (QDs) in the field of an ultrashort and ultrafast circularly polarized optical pulse. The QDs have the shape of a disk and their electron systems are described within an effective model with infinite mass boundary conditions. Similar to TMDC monolayers, a circularly polarized pulse generates ultrafast valley polarization of such QDs. The dependence of the valley polarization on the size of the dot is sensitive to the dot material and, for different materials, show both monotonic increase with the dot radius and nonmonotonic behavior with a local maximum at a finite dot radius.

The gravitational Vlasov-Poisson system with infinite mass and velocities in $\mathbb{R}^3$

The gravitational Vlasov-Poisson system with infinite mass and velocities in $\mathbb{R}^3$

TRANSIENT ANALYSIS OF LIQUID-HYDROGEN TRANSFER IN CRYOGENIC STORAGE TANKS

Efficient transfer of liquid hydrogen is critical for a myriad of processes in terrestrial and extraterrestrial applications. The objective of this study is to model and quantify the amount of liquid parahydrogen vaporized during a discharging/charging process in a cryogenic storage system. The effects that are included include geometrical effects (storage tank volume), two-phase compressible flow, choking/unchoking, and wall-fluid heat transfer. A brief description of other physical boil-off mechanisms is also presented. This study provides a foundation for applicationspecific optimization. The storage system studied comprises two interconnected tanks whose transfer line has a variation in the flow area. This simulates current liquid-hydrogen storage and transportation systems. The model tracks the temperature- and pressure-time histories of liquid hydrogen as it flows between storage tanks, in both the choked and unchoked flow regimes. The transfer of liquid is induced solely by the pressure differential that exists between the two storage tanks. An iterative technique helps account for choking, which is likely to exist at the throat in two-phase flow. Cases of zero and infinite tank-wall thermal mass are also discussed. By analyzing the behavior of fundamental variables during the transient transfer of liquid hydrogen, boil-off losses may be minimized if the variables with the greatest effect on boil-off losses are controlled.

Event-by-event heavy-flavour dynamics: Estimating the spatial diffusion coefficient Ds from charm to the infinite mass limit

Quasi-Particle Model (QPM) has been developed to study charm quark dynamics in ultra-relativistic heavy-ion collisions with good description of D mesons RAA(pT) and v2,3(pT) and leading to the evaluation of the spatial diffusion coefficient Ds(T). With an event-by-event full Boltzmann transport approach followed by a hybrid hadronization via coalescence plus fragmentation, we show RAA(pT), v2(pT) down to pT → 0 for D and B mesons. We find that QPM approach is able to correctly predict first available data on RAA(pT) and v2(pT) of single-electron from B mesons decays measured by ALICE. A significant breaking of the expected scaling of the thermalization time τth with MQ/T is found. Charm quark Ds(T) is about 50% larger than the asymptotic value for MQ → ∞, while the bottom Ds(T) is only 20% higher. In the infinite mass limit the Ds(T) is consistent with recent lQCD calculations with dynamical quarks.

Nonlinear enhanced dissipation in viscous Burgers type equations II

In this follow up but self contained paper, we focus on the viscous Burgers equation. There, using the Hopf-Cole transformation, we compute the long time behavior of solutions for some classes of infinite mass initial datas. We show that an enhanced dissipation effect occurs generically, that is the decay rate in time is better than if we considered instead the heat equations for the same inital value. We also show the existence of a kind of global attractor per class.

Schwarzschild Black Holes in Extended Spacetime with Two Time Dimensions

Black holes are one of the most extreme phenomena in the Universe, bridging the gap between the realms of general relativity and quantum physics. Any matter that crosses the event horizon moves towards the core of the black hole, creating a singularity with infinite mass density—a phenomenon that cannot be comprehended within present theories of relativity and quantum physics. In this study, we undertake an investigation of non-rotating, non-charged Schwarzschild black holes in an extended spacetime framework with two time dimensions. To accomplish this, we extend Einstein’s field equations by one more temporal dimension. We solve the corresponding equations for a spherical central mass, which leads to an Abel-type equation for the 5D Schwarzschild metric. By exploring distinct solution classes, we present an approximate solution for the 5D metric. Our proposed solution maintains consistency with Schwarzschild’s 4D solution. Finally, we address the central black hole singularity and demonstrate a potential breakthrough, as our solution effectively avoids the singularity quandary, providing valuable insight into the fundamental properties of black holes in this augmented framework.

The seed-to-solution method for the Einstein constraints and the asymptotic localization problem

We establish the existence of a broad class of asymptotically Euclidean solutions to Einstein's constraint equations, whose asymptotic behavior at infinity is prescribed arbitrarily. The proposed seed-to-solution method encompasses vacuum as well as matter spaces, and relies on iterations based on the linearized Einstein operator and its dual. It generates a Riemannian manifold (with finitely many asymptotically Euclidean ends) from any seed data set consisting of(1) a Riemannian metric and a symmetric two-tensor and(2) a (density) field and a (momentum) vector field representing the matter content. We distinguish between tame or strongly tame seed data sets, depending whether the data provides a rough or an accurate asymptotic Ansatz at infinity. We encompass classes of metrics and matter fields with low decay (possibly with infinite ADM mass) or strong decay (with Schwarzschild behavior). Our analysis is motivated by Carlotto and Schoen's pioneering work on the localization problem for Einstein's vacuum equations. Dealing with metrics with low decay and, simultaneously, establishing estimates that include (and go beyond) harmonic decay require significantly new arguments which are developed in the present paper. We work in a weighted Lebesgue-Hölder framework adapted to the given seed data, and we analyze the nonlinear coupling between the Hamiltonian and momentum constraints. By establishing elliptic regularity estimates for the linearized Einstein operator and its dual, we uncover the novel notion of mass-momentum correctors which is related to the ADM mass-momentum of the manifold. We derive precise estimates for the difference between the seed data and the associate Einstein solution —a result that should be of interest for future numerical investigations. Furthermore, we introduce here and study the asymptotic localization problem in which we replace Carlotto-Schoen's exact localization requirement by an asymptotic condition at a super-harmonic rate. By applying our seed-to-solution method with a suitably constructed, parametrized family of seed data, we solve this problem by exhibiting mass-momentum correctors with harmonic decay.

Classical spin gravitational Compton scattering

We introduce a novel bootstrap method for heavy-mass effective field theory classical Compton scattering amplitudes involving two massless particles and two arbitrary-spin infinite-mass limit particles. Using a suitable ansatz, we deduce new and explicit classical spin results for gluon four and five-point infinite mass processes that exhibit a certain exponentiated three-point tree-level factorizations and feature no spurious poles. We discuss the generalization of our bootstrap to higher multiplicities and summarize future potential applications.

The Ultimate Speed of an accelerated Electron without Infinite Mass

Failure to accelerate electrons beyond the speed of light, led to special relativity, where mass increases with speed, becoming infinitely large at the speed of light. Invoking aberration of electric field, this paper introduces radiative electrodynamics where an electron is accelerated to the speed of light at constant mass and with emission of radiation. The accelerating force on an electron moving in an electric field, is less than the force on a stationary one, relative to an observer. This difference is radiation reaction force, something akin to frictional force, against which work done appears as radiation. An accelerated electron moves in an electric field, with constant mass as the rest mass, emitting radiation equal to the difference between change in potential energy and change in kinetic energy. Circular revolution of an electron, in an atom, round the central force of attraction of a nucleus, as in the Rutherford’s nuclear model of the hydrogen atom, is shown to be without radiation and inherently stable. Emission of radiation takes place if the electron in an atom is dislodged from a circular orbit. It then moves in an elliptic path, emitting radiation, at the frequency of revolution, with fine structure, before reverting to a circular orbit. Describing aberration of electric field, introducing radiative electrodynamics, obtaining the ultimate of speed of light outside special relativity, and getting radiation from accelerated electrons outside quantum mechanics, are notable results of this paper.

Two-loop helicity amplitudes for H+jet production to higher orders in the dimensional regulator

In view of the forthcoming High-Luminosity phase of the LHC, next-to-next-to-next-to-leading (N3LO) calculations for the most phenomenologically relevant processes become necessary. In this work, we take the first step towards this goal for H+jet production by computing the one- and two-loop helicity amplitudes for the two contributing processes, H → ggg, Hto qoverline{q}g , in an effective theory with infinite top quark mass, to higher orders in the dimensional regulator. We decompose the amplitude in scalar form factors related to the helicity amplitudes and in a new basis of tensorial structures. The form factors receive contributions from Feynman integrals which were reduced to a novel canonical basis of master integrals. We derive and solve a set of differential equations for these integrals in terms of Multiple Polylogarithms (MPLs) of two variables up to transcendental weight six.