Momentum Variables Research Articles

Three point energy correlators in the collinear limit: symmetries, dualities and analytic results

Energy Correlators measure the energy deposited in multiple detectors as a function of the angles between the detectors. In this paper, we analytically compute the three particle correlator in the collinear limit in QCD for quark and gluon jets, and also in mathcal{N} = 4 super Yang-Mills theory. We find an intriguing duality between the integrals for the energy correlators and infrared finite Feynman parameter integrals, which maps the angles of the correlators to dual momentum variables. In mathcal{N} = 4, we use this duality to express our result as a rational sum of simple Feynman integrals (triangles and boxes). In QCD our result is expressed as a sum of the same transcendental functions, but with more complicated rational functions of cross ratio variables as coefficients. Our results represent the first analytic calculation of a three-prong jet substructure observable of phenomenological relevance for the LHC, revealing unexplored simplicity in the energy flow of QCD jets. They also provide valuable data for improving the understanding of the light-ray operator product expansion.

A staggered semi-implicit hybrid FV/FE projection method for weakly compressible flows

In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in [1,2] for viscous incompressible flows is extended here to solve the compressible Navier-Stokes equations. Instead of considering the classical system including the energy conservation equation, we replace it by the pressure evolution equation written in non-conservative form. To ease the discretization of complex spatial domains, face-type unstructured staggered meshes are considered. A projection method allows the decoupling of the computation of the density and linear momentum variables from the pressure. Then, an explicit finite volume scheme is used for the resolution of the transport diffusion equations on the dual mesh, whereas the pressure system is solved implicitly by using continuous finite elements defined on the primal simplex mesh. Consequently, the CFL stability condition depends only on the flow velocity, avoiding the severe time restrictions that might be imposed by the sound velocity in the weakly compressible regime. High order of accuracy in space and time of the transport diffusion stage is attained using a local ADER (LADER) methodology. Moreover, also the CVC Kolgan-type second order in space and first order in time scheme is considered. To prevent spurious oscillations in the presence of shocks, an ENO-based reconstruction, the minmod limiter or the Barth-Jespersen limiter are employed. To show the validity and robustness of our novel staggered semi-implicit hybrid FV/FE scheme, several benchmarks are analysed, showing a good agreement with available exact solutions and numerical reference data from low Mach numbers, up to Mach numbers of the order of unity.

Cylindrical porous radiant burner with internal combustion regime: Energy saving analysis using response surface method

Abstract A response surface analysis is performed on a cylindrical porous radiant burner with internal combustion regime, which is recently introduced. A structured grid is used to perform the simulations. First, the equations of continuity, momentum, turbulence, energy, radiation, mixture fraction and progress variable were solved with an appropriate accuracy. An excellent agreement was observed between the numerical results and the available laboratory data. Second, three response surfaces of the output enthalpy, radiant efficiency and radiative heat were investigated using the verified model. The independent variables including input power, porous foam’s emissivity and the equivalence ratio are changed in the ranges of P ∈ [1.5,5] kW, erad ∈ [0.4,0.9] and φ ∈ [0.5,1.1], respectively. The results show that the radiant efficiency of above 50% can be achieved using this type of porous burner with no preheating. Based on a local sensitivity analysis, the sensitivity of ηrad to erad and φ at (P,erad,φ) = (5,0.4,0.8) is equal to 7.50% and 0.511%, according to the coded independent variables, respectively. Moreover, according to an energy saving analysis, for a radiant heat of 900 W, 13.6% of energy could be saved compared to the ideal conditions, in which φ ≈ 1, by choosing the best conditions.

Noncommutative black holes of various genera in the connection formalism

We consider black hole interiors of arbitrary genus number within the paradigm of non-commutative geometry. The study is performed in two ways: One way is a simple smearing of a matter distribution within the black hole. The resulting structure is often known in the literature as a "model inspired by non-commutative geometry". The second method involves a more fundamental approach, in which the Hamiltonian formalism is utilized and a non-trivial Poisson bracket is introduced between the configuration degrees of freedom, as well as between the canonical momentum degrees of freedom. This is done in terms of connection variables instead of the more common ADM variables. Connection variables are utilized here since non-commutative effects are usually inspired from the quantum theory, and it is the connection variables that are used in some of the more promising modern theories of quantum gravity. We find that in the first study, the singularity of the black holes can easily be removed. In the second study, we find that introducing a non-trivial bracket between the connections (the configuration variables) may delay the singularity, but not necessarily eliminate it. However, by introducing a non-trivial bracket between the densitized triads (the canonical momentum variables) the singularity can generally be removed. In some cases, new horizons also appear due to the non-commutativity.

Renormalization and scale evolution of the soft-quark soft function

Soft functions defined in terms of matrix elements of soft fields dressed by Wilson lines are central components of factorization theorems for cross sections and decay rates in collider and heavy-quark physics. While in many cases the relevant soft functions are defined in terms of gluon operators, at subleading order in power counting soft functions containing quark fields appear. We present a detailed discussion of the properties of the soft-quark soft function consisting of a quark propagator dressed by two finite-length Wilson lines connecting at one point. This function enters in the factorization theorem for the Higgs-boson decay amplitude of the h → γγ process mediated by light-quark loops. We perform the renormalization of this soft function at one-loop order, present a conjecture for its two-loop anomalous dimension and discuss solutions to its renormalization-group evolution equation in momentum space, in Laplace space and in the “diagonal space”, where the evolution is strictly local in the momentum variable.

Nonexistence of global characteristics for viscosity solutions

Two different types of generalized solutions, namely viscosity and variational solutions, were introduced to solve the first-order evolutionary Hamilton--Jacobi equation. They coincide if the Hamiltonian is convex in the momentum variable. In this paper we prove that there exists no other class of integrable Hamiltonians sharing this property. To do so, we build for any non-convex non-concave integrable Hamiltonian a smooth initial condition such that the graph of the viscosity solution is not contained in the wavefront associated with the Cauchy problem. The construction is based on a new example for a saddle Hamiltonian and a precise analysis of the one-dimensional case, coupled with reduction and approximation arguments.

Towards Gaussian states for loop quantum gravity

An important challenge in loop quantum gravity is to find semiclassical states - states that are as close to classical as quantum theory allows. This is difficult because the states in the Hilbert space used in LQG are excitations over a vacuum in which geometry is highly degenerate. Additionally, fluctuations are distributed very unevenly between configuration and momentum variables. Coherent states that have been proposed to balance the uncertainties more evenly can, up to now, only do this for finitely many degrees of freedom. Our work is motivated by the desire to obtain Gaussian states that encompass all degrees of freedom. To obtain a toy-model we reformulate the U(1) holonomy-flux algebra in any dimension as a Weyl algebra, and discuss generalisations to SU(2). We then define and investigate a new class of states on these algebras which behave like quasifree states on the momentum variables.

Nonstandard caustics for localized solutions of the 2d shallow water equations with applications to wave propagation and run-up on a shallow beach

The usual semiclassical approximation is not directly applicable to linearized two-dimensional shallow water equations with localized initial data describing long waves (for example, tsunami waves) in a bounded basin of variable depth, because the momentum variables on the geometric optics rays become infinite at the boundary of the region. To obtain asymptotic solutions, one needs to extend the phase space and introduce a modified Maslov canonical operator. The paper gives a brief survey of some results obtained in this direction by the authors and their colleagues.

Strong mechanical squeezing in an optomechanical system based on Lyapunov control

We propose a scheme to generate strong squeezing of a mechanical oscillator in an optomechanical system through Lyapunov control. Frequency modulation of the mechanical oscillator is designed via Lyapunov control. We show that the momentum variance of the mechanical oscillator decreases with time evolution in a weak coupling case. As a result, strong mechanical squeezing is realized quickly (beyond 3 dB). In addition, the proposal is immune to cavity decay. Moreover, we show that the obtained squeezing can be detected via an ancillary cavity mode with homodyne detection.

Simulasi Pergerakan Tumpahan Minyak di Laut dengan Pengaruh Angin

As a petroleum-producing country, Indonesia has a very important role in supplying national and international petroleum needs. The distribution of oil by sea raises the risk of spills and harms the marine environment, especially for marine life. Most oil spills in the marine environment can form a thin layer on the surface due to the movement of wind, waves, and currents. In this study, the oil spill movement model used the Shallow Water Equation (SWE) model and the equation for the movement of oil spills. The SWE model consists of the equation of mass and momentum derived from the law of conservation of mass which is derived into the equation of continuity and the law of conservation of momentum which is derived into the equation of conservation of momentum. In this model, ocean currents are affected by several disturbances in the form of wind gusts and friction with the bottom. The model is solved numerically through simulation using the finite volume method. Discretization is done by using a staggered grid approach, where the mass and momentum variables are discretized in different cells. From the simulation results, it appears that the movement of oil spills is influenced by wind direction and current. The simulation results also found that the speed of the movement of oil spills has increased in the early times, but then gradually.

Pushing the limit of quantum transport simulations

Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient general-purpose algorithms have a computational cost that scales as $L^{6 \dots 7}$ in 3D, which on the one hand is a substantial improvement over older algorithms, but on the other hand still severely restricts the size of the simulation domain, limiting the usefulness of simulations through strong finite-size effects. Here, we present a novel class of algorithms that, for certain systems, allows to directly access the thermodynamic limit. Our approach, based on the Green's function formalism for discrete models, targets systems which are mostly invariant by translation, i.e. invariant by translation up to a finite number of orbitals and/or quasi-1D electrodes and/or the presence of edges or surfaces. Our approach is based on an automatic calculation of the poles and residues of series expansions of the Green's function in momentum space. This expansion allows to integrate analytically in one momentum variable. We illustrate our algorithms with several applications: devices with graphene electrodes that consist of half an infinite sheet; Friedel oscillation calculations of infinite 2D systems in presence of an impurity; quantum spin Hall physics in presence of an edge; the surface of a Weyl semi-metal in presence of impurities and electrodes connected to the surface. In this last example, we study the conduction through the Fermi arcs of the topological material and its resilience to the presence of disorder. Our approach provides a practical route for simulating 3D bulk systems or surfaces as well as other setups that have so far remained elusive.

Axion-like-particle decay in strong electromagnetic backgrounds

The decay of a massive pseudoscalar, scalar and U(1) boson into an electron-positron pair in the presence of strong electromagnetic backgrounds is calculated. Of particular interest is the constant-crossed-field limit, relevant for experiments that aim to measure high-energy axion-like-particle conversion into electron-positron pairs in a magnetic field. The total probability depends on the quantum nonlinearity parameter — a product of field and lightfront momentum invariants. Depending on the seed particle mass, different decay regimes are identified. In the below-threshold case, we find the probability depends on a non-perturbative tunneling exponent depending on the quantum parameter and the particle mass. In the above-threshold case, we find that when the quantum parameter is varied linearly, the probability oscillates nonlinearly around the spontaneous decay probability. A strong-field limit is identified in which the threshold is found to disappear. In modelling the fall-off of a quasi-constant-crossed magnetic field, we calculate probabilities beyond the constant limit and investigate when the decay probability can be regarded as locally constant.

The momentum representation of the hydrogen atom in paraboloidal coordinates

We examine the procedure to construct the variables of use for the momentum representation in quantum mechanics. The momentum variables must be chosen properly conjugate to the corresponding position space variables, such that valid uncertainty relationships are maintained. We then apply such considerations to the hydrogen atom to obtain the momentum space wave functions corresponding to the position space functions in paraboloidal coordinates. The advantages and disadvantages of employing the momentum representation are explored.

Relativistic deformed kinematics from momentum space geometry

We present a way to derive a deformation of special relativistic kinematics (possible low energy signal of a quantum theory of gravity) from the geometry of a maximally symmetric curved momentum space. The deformed kinematics is fixed (up to change of coordinates in the momentum variables) by the algebra of isometries of the metric in momentum space. In particular, the well-known example of $\kappa$-Poincar\'e kinematics is obtained when one considers an isotropic metric in de Sitter momentum space such that translations are a subgroup of the isometry group, and for a Lorentz covariant algebra one gets the also well-known case of Snyder kinematics. We prove that our construction gives generically a relativistic kinematics and explain how it relates to previous attempts of connecting a deformed kinematics with a geometry in momentum space.

Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100 % condensed. Finally, we also explore inter-connections between the variances.

Many-body quantum dynamics of an asymmetric bosonic Josephson junction

The out-of-equilibrium quantum dynamics of an interacting Bose gas trapped in a one-dimensional asymmetric double-well potential is studied by solving the many-body Schrödinger equation numerically accurately. We examine how the gradual loss of symmetry of the confining trap affects the macroscopic quantum tunneling dynamics of the system between the two wells. In an asymmetric double well, the two wells are not equivalent anymore, say, the left well is deeper than the right one. Accordingly, we analyze the dynamics by initially preparing the condensate in both the left and the right wells. The dynamics of the system is characterized by the time evolution of a few physical quantities of increasing many-body complexity, namely, the survival probability, depletion and fragmentation, and the many-particle position and momentum variances. In particular, we have examined the frequencies and amplitudes of the oscillations of the survival probabilities, the time scale for the development of fragmentation and its degree, and the growth and oscillatory behavior of the many-particle position and momentum variances. There is an overall suppression of the oscillations of the survival probabilities in an asymmetric double well, except for resonant values of asymmetry for which the one-body ground state energy in the right well matches with one of the one-body excited states in the left well, thereby resulting in resonantly enhanced tunneling from the right well ground state. Overall, depending on whether the condensate is initially prepared in the left or right well, the repulsive inter-atomic interactions affect the survival probabilities differently. For a sufficiently strong repulsive interaction, the system is found to become fragmented. The degree of fragmentation depends both on the asymmetry of the trap and the initial well in which the condensate is prepared in a non-trivial manner. Furthermore, we show that the phenomenon of resonantly enhanced tunneling can be accompanied by a large degree of fragmentation (depletion) for the strong (weak) interaction. The many-particle position and momentum variances follow the density oscillations of the system in the asymmetric double well and bears prominent signatures of the degree of depletion or fragmentation, depending on the strength of the interactions. These quantities further exhibit a fine structure signifying a breathing-mode oscillation. Finally, a universality of fragmentation for systems made of different numbers of particles but the same interaction parameter is also found and its dependence on the asymmetry is investigated. The phenomenon is robust despite the asymmetry of the junction and admits a macroscopically-large fragmented condensate characterized by a diverging many-particle position variance. This is as far as one can get from the dynamics of the density in the junction.

Effect of dynamical noncommutativity on the limiting mass of white dwarfs

The discovery of the existence of an upper bound on the mass of a white dwarf star is considered as one of the finest of twentieth century astrophysics. On approaching this limiting mass of 1.4M⊙, known as the Chandrasekhar mass-limit, a white dwarf is believed to spark off with an explosion called type Ia supernova, which is considered to be a standard candle. But since the last decade, observations of several over-luminous, peculiar type Ia supernovae indicate that the Chandrasekhar-limit be significantly larger. By postulating noncommutativity between the components of momentum variables, we show that the mass of white dwarfs can be enhanced significantly and arrive at a new super-Chandrasekhar mass limit of about 4.68M⊙. This can provide a plausible explanation for the origin of over-luminous peculiar type Ia supernovae.

On a measurement approach to support evaluation of thermal scattering law data

Inelastic thermal neutron scattering in materials that act as neutron moderators, reflectors, and filters results in shaping the neutron spectrum at low energies. This phenomenon is described using differential scattering cross sections calculated from three components including the bound atom (i.e., nuclear) scattering cross section of the neutron, the ratio of the outgoing and incoming neutron energy, and the thermal scattering law (TSL), i.e., S(α,β), where α and β represent dimensionless momentum and energy exchange variables, respectively. To date, no TSL libraries are generated using measured data. However, valuable information may be derived from measurements and “targeted” experiments that can validate TSL data and the related inelastic scattering cross sections. As a demonstration, a suite of coordinated measurements and experiments is described that was designed and used to support the evaluation of the TSL for “nuclear” graphite. This experimental suite includes neutron powder diffraction (for structure analysis), positron annihilation (for nano porosity assessment), inelastic neutron scattering measurements using a chopper spectrometer, transmission experiments using neutrons with energy below the Bragg cutoff thereby accessing the total (inelastic) cross section, and a slowing-down-time experiment to observe the developing neutron spectrum in the material. This experimental suite was key to understanding the difference in TSL between “nuclear” and “ideal” graphite and for the inclusion of “nuclear” graphite in the ENDF/B-VIII.0 nuclear data library release.

Testing the Four Factors of the Carhart Model Against Excess Return of Shares in Companies Registered in the Kompas 100 Index for the 2014-2016 Period

The researcher intends to test the four carhart factor model of stock excess return in companies incorporated in Kompas 100 for the 2014-2016 period. Regression analysis was performed on four carhart factor models, namely market returns, firm size, book to market, and momentum towards excess return. The results of this study indicate that in the partial hypothesis testing market return, firm size, and book to market equty variables significantly influence the excess return, while the momentum variable does not significantly influence the magnitude of excess return.Keywords: Four factors, market returns, firm size, book to market equity, momentum, excess stock returns

Global Stability of Minkowski Space for the Einstein\u2013Vlasov System in the Harmonic Gauge

Minkowski space is shown to be globally stable as a solution to the massive Einstein–Vlasov system. The proof is based on a harmonic gauge in which the equations reduce to a system of quasilinear wave equations for the metric, satisfying the weak null condition, coupled to a transport equation for the Vlasov particle distribution function. Central to the proof is a collection of vector fields used to control the particle distribution function, a function of both spacetime and momentum variables. The vector fields are derived using a general procedure, are adapted to the geometry of the solution and reduce to the generators of the symmetries of Minkowski space when restricted to acting on spacetime functions. Moreover, when specialising to the case of vacuum, the proof provides a simplification of previous stability works.