Finite Mass Research Articles

Transport inequalities for random point measures

We derive transport-entropy inequalities for mixed binomial point processes, and for Poisson point processes. We show that when the finite intensity measure satisfies a Talagrand transport inequality, the law of the point process also satisfies a Talagrand type transport inequality. We also show that a Poisson point process (with arbitrary σ-finite intensity measure) always satisfies a universal transport-entropy inequality à la Marton. We explore the consequences of these inequalities in terms of concentration of measure and modified logarithmic Sobolev inequalities. In particular, our results allow one to extend a deviation inequality by Reitzner [33], originally proved for Poisson random measures with finite mass.

Holographic nuclear physics with massive quarks

We discuss nuclear physics in the Witten-Sakai-Sugimoto model, in the limit of large number $N_c$ of colors and large 't Hooft coupling, with the addition of a finite mass for the quarks. Individual baryons are described by classical solitons whose size is much smaller than the typical distance in nuclear bound states, thus we can use the linear approximation to compute the interaction potential and provide a natural description for lightly bound states. We find the classical geometry of nuclear bound states for baryon numbers up to B=8. The effect of the finite pion mass - induced by the quark mass via the GMOR relation - is to decrease the binding energy of the nuclei with respect to the massless case. We discuss the finite density case with a particular choice of a cubic lattice, for which we find the critical chemical potential, at which the hadronic phase transition occurs.

The quantum mass gap of extremal black holes

Using sophisticated string theory calculations, Maldacena and Susskind have intriguingly shown that near-extremal black holes are characterized by a finite mass gap above the corresponding zero-temperature (extremal) black-hole configuration. In the present compact paper we explicitly prove that the minimum energy gap Egap=ħ2/M3, which characterizes the mass spectra of near-extremal charged Reissner-Nordström black holes, can be inferred from a simple semi-classical analysis.

Nonvanishing finite scalar mass in flux compactification

We study possibilities to realize a nonvanishing finite Wilson line (WL) scalar mass in flux compactification. Generalizing loop integrals in the quantum correction to WL mass at one-loop, we derive the conditions for the loop integrals and mode sums in one-loop corrections to WL scalar mass to be finite. We further guess and classify the four-point and three-point interaction terms satisfying these conditions. As an illustration, the nonvanishing finite WL scalar mass is explicitly shown in a six dimensional scalar QED by diagrammatic computation and effective potential analysis. This is the first example of finite WL scalar mass in flux compactification.

Relaxation to Equilibrium in the One-Dimensional Thin-Film Equation with Partial Wetting and Linear Mobility

We investigate the large time behavior of compactly supported smooth solutions for a one-dimensional thin-film equation with linear mobility in the regime of partial wetting. We show the stability of steady state solutions. Relaxation rates are obtained for initial data which are close to a steady state in a suitable sense. The proof uses the Lagrangian coordinates. Our method is to establish and exploit differential relations between the energy and the dissipation as well as some interpolation inequalities. Our result is different from earlier results because here we consider solutions with finite mass.

Position-dependent finite symmetric mass harmonic like oscillator: Classical and quantum mechanical study

Abstract We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechanical phase space for necessary comparison with the same obtained classically. The phase portrait in all the cases exhibited closed loop reflecting the stable system but the quantum phase portrait exhibited the inherent signature (cusp or kink) near origin associated with the mass. Although the systems possess periodic motion, the discrete eigenvalues do not possess any similarity with that of the simple harmonic oscillator having m = 1.

Two-body problem in a multiband lattice and the role of quantum geometry

We consider the two-body problem in a periodic potential, and study the bound-state dispersion of a spin-$\uparrow$ fermion that is interacting with a spin-$\downarrow$ fermion through a short-range attractive interaction. Based on a variational approach, we obtain the exact solution of the dispersion in the form of a set of self-consistency equations, and apply it to tight-binding Hamiltonians with onsite interactions. We pay special attention to the bipartite lattices with a two-point basis that exhibit time-reversal symmetry, and show that the lowest-energy bound states disperse quadratically with momentum, whose effective-mass tensor is partially controlled by the quantum metric tensor of the underlying Bloch states. In particular, we apply our theory to the Mielke checkerboard lattice, and study the special role played by the interband processes in producing a finite effective mass for the bound states in a non-isolated flat band.

An efficient and sustainable approach for cooling underground substations

With rapid rates of urbanisation and significant improvements in construction technologies, the number of subsurface infrastructure projects has drastically increased in recent years. In addition to their primary functions, these structures have shown great potential as energy geo-structures, exchanging heat with the ground to heat and cool spaces. Given their large contact area with the ground, energy tunnels are proving to be a sustainable source of thermal energy for effectively heating under- and above-ground spaces. However, their efficiency in cooling-dominated conditions has not yet been adequately studied. This paper tackles one of the key challenges regarding transport tunnels: sustainable cooling of underground substations, by introducing an efficient and cost-effective cooling method. The method takes advantage of airflow in the tunnels and relatively stable ground temperatures and involves heat exchangers in the form of water-filled high-density polyethylene (HDPE) pipes being integrated into the tunnel space. The efficiency of the proposed system is numerically assessed by analysing the spatio-temporal variations of temperature in the ground, substation, tunnel air, tunnel structure and heat exchangers caused by continuous heat rejection from the substations. A detailed 3D finite element heat and mass transport model is used, and alternative placements of heat exchangers are investigated. Results show that heat exchangers placed on the tunnel lining, and hence exposed to the tunnel airflow, could efficiently supply a substation’s cooling demand, without significantly increasing the temperature of the tunnel air or the ground. The substantial economic benefits of this cooling system compared to a conventional cooling system is also demonstrated.

The strong Lp-closure of vector fields with finitely many integer singularities on B3

This paper is aimed to investigate the strong Lp-closure LZp(B) of the vector fields on the open unit ball B⊂R3 that are smooth up to finitely many integer point singularities. First, such strong closure is characterized for arbitrary p∈[1,+∞). Secondly, it is shown what happens if the integrability order p is large enough (namely, if p⩾3/2). Eventually, a decomposition theorem for elements in LZ1(B) is given, conveying information about the possibility of connecting the singular set of such vector fields by a mass-minimizing, integer 1-current on B with finite mass.

QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider

Using Soft-Collinear Effective Theory, we develop the transverse-momentum-dependent factorization formalism for heavy flavor dijet production in polarized-proton-electron collisions. We consider heavy flavor mass corrections in the collinear-soft and jet functions, as well as the associated evolution equations. Using this formalism, we generate a prediction for the gluon Sivers asymmetry for charm and bottom dijet production at the future Electron-Ion Collider. Furthermore, we compare theoretical predictions with and without the inclusion of finite quark masses. We find that the heavy flavor mass effects can give sizable corrections to the predicted asymmetry.

Confined variational calculations of low-energy electron-helium scattering

The $S\text{\ensuremath{-}},$ $P\text{\ensuremath{-}},$ and $D\text{\ensuremath{-}}\mathrm{wave}$ elastic scattering of electrons by atomic helium with the scattering energy between 0.136 and $16.463\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ is studied using the confined variational method. Our calculated phase shifts improve the best published results by at least one order of magnitude. The finite nuclear mass effect on the $S$-wave phase shift at very low scattering energy between 0.022 and $0.067\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ is investigated, and the accurate $S$-wave scattering length is determined to be $1.1723{a}_{0}$, where ${a}_{0}$ is the Bohr radius. The results reported here can serve as a benchmark for other theoretical and experimental studies.

Gluon polarization tensor and dispersion relation in a weakly magnetized medium

We study the polarization and dispersion properties of gluons moving within a weakly magnetized background at one-loop order. To this end, we show two alternative derivations of the charged fermion propagator in the weak field expansion and use this expression to compute the lowest order magnetic field correction to the gluon polarization tensor. We explicitly show that, in spite of its cumbersome appearance, the gluon polarization tensor is transverse as required by gauge invariance. We also show that none of the three polarization modes develops a magnetic mass and that gluons propagate along the light cone, non withstanding that Lorentz invariance is lost due to the presence of the magnetic field. By comparing with the expression for the gluon polarization tensor valid to all orders in the magnetic field, the existence of a second solution, corresponding to a finite gluon mass, is shown to be spurious and an artifact of the lowest order approximation in the field strength. We also study the strength of the polarization modes for real gluons. We conclude that, provided the spurious solutions are discarded, the lowest order approximation to the gluon polarization and dispersion properties is good as long as the field strength is small compared to the loop fermion mass.

Hyperfine structure of the 2P3 state in Be9 and the nuclear quadrupole moment

We have performed accurate calculations of the hyperfine structure of the $2\,^3\!P$ state in the $^9$Be atom with the help of highly optimized, explicitly correlated functions, accounting for the leading finite nuclear mass, radiative, nuclear structure and relativistic effects. By comparison with measurements, we have determined the $^9$Be nuclear quadrupole moment to be $Q_{\rm N} = 0.05350(14)$ barns, which is not only the most accurate result, but also disagrees with previous determinations.

Discrete Versions of Jensen-Fisher, Fisher and Bayes-Fisher Information Measures of Finite Mixture Distributions.

In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback–Leibler, Jeffreys and Jensen–Shannon divergences.

Magic wavelengths for the helium 23S1→21P1 forbidden transition

A series of magic wavelengths for the forbidden transition of $2{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{1}{P}_{1}$ in helium are determined by performing large-scale full relativistic configuration interaction calculations based on Dirac-Coulomb-Breit Hamiltonian with the mass shift operator included. QED corrections to magic wavelengths are taken into account by using the perturbation theory in nonrelativistic configuration interaction calculations. The 1335.55(2)-nm magic wavelength for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}(M=\ifmmode\pm\else\textpm\fi{}1)\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{1}{P}_{1}(M=0)$ transition is found to be sensitive to the finite nuclear mass, relativistic, and QED effects, and its measurement might provide a test of atomic structure theory.

Traversable Wormholes in Einstein-Dirac-Maxwell Theory.

We construct a specific example of a class of traversable wormholes in Einstein-Dirac-Maxwell theory in four spacetime dimensions, without needing any form of exotic matter. Restricting to a model with two massive fermions in a singlet spinor state, we show the existence of spherically symmetric asymptotically flat configurations which are free of singularities, representing localized states. These solutions satisfy a generalized Smarr relation, being connected with the extremal Reissner-Nordström black holes. They also possess a finite mass M and electric charge Q_{e}, with Q_{e}/M>1. An exact wormhole solution with ungauged, massless fermions is also reported.

Dirac Equation-Based Formulation for the Quantum Conductivity in 2D-Nanomaterials

Starting from the four component-Dirac equation for free, ballistic electrons with finite mass, driven by a constant d.c. field, we derive a basic model of scalar quantum conductivity, capable of yielding simple analytic forms, also in the presence of magnetic and polarization effects. The classical Drude conductivity is recovered as a limit case. A quantum-mechanical evaluation is provided for parabolic and linear dispersion, as in graphene, recovering currently used expressions as particular cases. Numerical values are compared with the ones from the literature in the case of graphene under d.c. applied field. In particular, the effect of the sample length and field strength on the conductivity are highlighted.

The renormalised mathrm{O}(a) improved vector current in three-flavour lattice QCD with Wilson quarks

We present the results of a non-perturbative determination of the improvement coefficient c_mathrm{V} and the renormalisation factor Z_mathrm{V}, which define the renormalised vector current in three-flavour mathrm{O}(a) improved lattice QCD with Wilson quarks and tree-level Symanzik-improved gauge action. In case of the improvement coefficient, we consider both lattice descriptions of the vector current, the local as well as the conserved (i.e., point-split) one. Our improvement and normalisation conditions are based on massive chiral Ward identities and numerically evaluated in the Schrödinger functional setup, which allows to eliminate finite quark mass effects in a controlled way. In order to ensure a smooth dependence of the renormalisation constant and improvement coefficients on the bare gauge coupling, our computation proceeds along a line of constant physics, covering the typical range of lattice spacings 0.04,mathrm{fm}lesssim alesssim 0.1,mathrm{fm} that is useful for phenomenological applications. Especially for the improvement coefficient of the local vector current, we report significant differences between the one-loop perturbative estimates and our non-perturbative results.

A Simple Model Approach to Dilepton Production Rate in Relativistic Heavy Ion Collisions

We compute the dilepton production rate from deconfined phase of quark-gluon plasma using the quasi-particle model (QPM). The computation is based on an extension of our previous work. In this model, the finite quark mass is replaced by the effective quark mass which is considered as the sum of square of current mass, coupling of thermal and current mass and square of thermal mass. This leads to the modest enhancement in the dilepton production rate. The results indicate that the emission rate is also an increasing function of chemical potential. The study implies that the model results are significantly enhanced with the effective quark mass as compared to thermal quark mass in the low mass region and not altered in the intermediate mass region. So the model using the effective quark mass fits well in the production of dilepton rates.

Updated constraints on massive neutrino self-interactions from cosmology in light of the H0 tension

We have updated the constraints on flavour universal neutrino self-interactions mediated by a heavy scalar, in the effective 4-fermion interaction limit. We use the relaxation time approximation to modify the collisional neutrino Boltzmann equations, which is known to be very accurate for this particular scenario. Based on the latest CMB data from the Planck 2018 data release as well as auxiliary data we confirm the presence of a region in parameter space with relatively strong self-interactions which provides a better than naively expected fit. However, we also find that the most recent data, in particular high-ℓ polarisation data from the Planck 2018 release, disfavours this solution even though it cannot yet be excluded. Our analysis takes into account finite neutrino masses (parameterised in terms of ∑ mν) and allows for a varying neutrino energy density (parameterised in terms of N eff), and we find that in all cases the neutrino mass bound inferred from cosmological data is robust against the presence of neutrino self-interactions. Finally, we also find that the strong neutrino self-interactions do not lead to a high value of H0 being preferred, i.e. this model is not a viable solution to the current H0 discrepancy.