Non-relativistic Regime Research Articles

The eikonal approach to gravitational scattering and radiation at mathcal{O} (G3)

Using mathcal{N} = 8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat mathcal{N} = 8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein’s gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.

Relativistic Treatment of Quantum Mechanical Gravitational-Harmonic Oscillator Potential

The solutions of the Klein- Gordon equation for the quantum mechanical gravitational plus harmonic oscillator potential with equal scalar and vector potential have been presented using the parametric Nikiforov-Uvarov method. The energy eigenvalues were obtained in relativistic and non-relativistic regime and the corresponding un-normalized eigenfunctions in terms of Laguerre polynomials. The numerical values for the S – wave bound state were obtained.

Convergence analysis of a symmetric exponential integrator Fourier pseudo-spectral scheme for the Klein–Gordon–Dirac equation

Recently, an exponential integrator Fourier pseudo-spectral (EIFP) scheme for the Klein–Gordon–Dirac (KGD) equation in the nonrelativistic limit regime has been proposed (Yi et al., 2019). The scheme is fully explicit and numerical experiments show that it is very efficient due to the fast Fourier transform (FFT). However, the authors did not give a strict convergence analysis and error estimate for the scheme. In addition, the scheme did not satisfy time symmetry which is an important characteristic of the exact solution. In this paper, by setting two-level format for Klein–Gordon part and three-level format for Dirac part, respectively, we proposed a new EIFP scheme for the KGD equation with periodic boundary conditions. The new scheme is time symmetric and fully explicit. By using the standard energy method and the mathematical induction, we make a rigorously convergence analysis and establish error estimates without any CFL condition restrictions on the grid ratio. The convergence rate of the proposed scheme is proved to be at the second-order in time and spectral-order in space, respectively, in a generic Hm-norm. The numerical experiments are carried out to confirm our theoretical analysis. Because that our error estimates are given under the general Hm-norm, the conclusion can easily be extended to two- and three-dimensional problems without the stability (or CFL) condition under sufficient regular conditions.

Radiation reaction from soft theorems

Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, in particular, to Einstein's gravity and to its Jordan-Brans-Dicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.

Chiral oscillations in the non-relativistic regime

Massive Dirac particles are a superposition of left and right chiral components. Since chirality is not a conserved quantity, the free Dirac Hamiltonian evolution induces chiral quantum oscillations, a phenomenon related to the Zitterbewegung, the trembling motion of free propagating particles. While not observable for particles in relativistic dynamical regimes, chiral oscillations become relevant when the particle’s rest energy is comparable to its momentum. In this paper, we quantify the effect of chiral oscillations on the non-relativistic evolution of a particle state described as a Dirac bispinor and specialize our results to describe the interplay between chiral and flavor oscillations of non-relativistic neutrinos: we compute the time-averaged survival probability and observe an energy-dependent depletion of the quantity when compared to the standard oscillation formula. In the non-relativistic regime, this depletion due to chiral oscillations can be as large as 40%. Finally, we discuss the relevance of chiral oscillations in upcoming experiments which will probe the cosmic neutrino background.

Revisiting Einstein's diffusion-mobility relation for universal quantum materials: A generalized paradigm

We have revisited the Einstein diffusion-mobility ratio, on the basis of the generalized Einstein relation, which quantifies both the quantum and classical levels of understanding on electron-hole dynamics in ordered and disordered materials. While the Einstein relation (diffusion-mobility ratio, D/) works only for classical systems under equilibrium cases, our generalized paradigm is quite general and works for systems ranging from classical to quantum systems in any dimensions. The proposed D/ formalism relies on the chemical potential which provides the cooperative nature between electronic and temperature counterparts on fundamental transport. Our generalized paradigm is applicable to both degenerate and non-degenerate cases, and explains the transition from linear to nonlinear relationship between the charge density and chemical potential. The symmetrical nature of electron-hole transport in highly degenerate two-dimensional quantum materials gives linear dispersion, preserving the time-reversal invariance property, while the symmetry is found to be broken in the nonlinear regime. Our generalized diffusion-mobility relation explains both the relativistic (Dirac particles) and non-relativistic regimes (Schrödinger particles) from low temperature to high temperature, and reproduces the classical Einstein relation in an appropriate limit.

Mapping the Dirac equation with spin and pseudospin symmetries in curved spacetime in the non-relativistic regime

Mapping the Dirac equation with spin and pseudospin symmetries in curved spacetime in the non-relativistic regime

Spherical accretion: Bondi, Michel, and rotating black holes

ABSTRACT In this work, we revisit the steady-state, spherically symmetric gas accretion problem from the non-relativistic regime to the ultrarelativistic one. We first perform a detailed comparison between the Bondi and Michel models, and show how the mass accretion rate in the Michel solution approaches a constant value as the fluid temperature increases, whereas the corresponding Bondi value continually decreases, the difference between these two predicted values becoming arbitrarily large at ultrarelativistic temperatures. Additionally, we extend the Michel solution to the case of a fluid with an equation of state corresponding to a monoatomic, relativistic gas. Finally, using general relativistic hydrodynamic simulations, we study spherical accretion on to a rotating black hole, exploring the influence of the black hole spin on the mass accretion rate, the flow morphology and characteristics, and the sonic surface. The effect of the black hole spin becomes more significant as the gas temperature increases and as the adiabatic index γ stiffens. For an ideal gas in the ultrarelativistic limit (γ = 4/3), we find a reduction of 10 per cent in the mass accretion rate for a maximally rotating black hole compared to a non-rotating one, while this reduction is of up to 50 per cent for a stiff fluid (γ = 2).

An adaptive mesh, GPU-accelerated, and error minimized special relativistic hydrodynamics code

ABSTRACT We present a new special relativistic hydrodynamics (SRHD) code capable of handling coexisting ultra-relativistically hot and non-relativistically cold gases. We achieve this by designing a new algorithm for conversion between primitive and conserved variables in the SRHD solver, which incorporates a realistic ideal-gas equation of state covering both the relativistic and non-relativistic regimes. The code can handle problems involving a Lorentz factor as high as 106 and optimally avoid the catastrophic cancellation. In addition, we have integrated this new SRHD solver into the code gamer (https://github.com/gamer-project/gamer) to support adaptive mesh refinement and hybrid OpenMP/MPI/GPU parallelization. It achieves a peak performance of 7 × 107 cell updates per second on a single Tesla P100 GPU and scales well to 2048 GPUs. We apply this code to two interesting astrophysical applications: (a) an asymmetric explosion source on the relativistic blast wave and (b) the flow acceleration and limb brightening of relativistic jets.

Solutions of the 2D Schrodinger equation and its thermal properties for improved ultra-generalized exponential hyperbolic potential (IUGE-HP)

In this research work, we investigate the 2D Schrodinger equation with improved ultra-generalized exponential-hyperbolic potential (IUGE-HP) is scrutinized taking into consideration the effects external magnetic and Aharonov–Bohm (AB) fields within the non-relativistic quantum mechanics regime. The Schrodinger equation in 2D for this consideration is solved using the asymptotic iteration method (AIM), and the energy equation and eigenfunction for the IUGE-HP in the presence of magnetic and AB fields are obtained in a compact form. The numerical energy spectra are analyzed, and it is observed that the presence of the external fields eliminates degeneracy from the spectra and the different values of the control parameter causes shifts in the energy spectra. The thermal and magnetic properties of the IUGE-HP in the presence of this external fields are duly investigated. The variations of the thermal and magnetic properties with control parameter are analyzed for negative \(\left( {\tau < 0} \right)\) and positive \(\left( {\tau > 0} \right)\). The present research finds applications in condensed matter, molecular and atomic physics, respectively.

Magnetic outflows from turbulent accretion disks

Context. Astrophysical disks are likely embedded in an ambient vertical magnetic field generated by its environment. This ambient field is known to drive magneto-rotational turbulence in the disk bulk, but it is also responsible for launching magnetised outflows at the origin of astrophysical jets. Yet, the interplay between turbulence and outflows is not understood. In particular, the vertical structure and long-term (secular) evolution of such a system lack quantitative predictions. It is, nevertheless, this secular evolution which is proposed to explain time variability in many accreting systems such as FuOr, X-ray binaries, and novae like systems. Aims. We seek to constraint the structure and long-term evolution of turbulent astrophysical disks subject to magnetised outflows in the non-relativistic regime. More specifically we aim to characterise the mechanism driving accretion, the dynamics of the disk atmosphere, the role played by the outflow, and the long-term evolution of mass and magnetic flux distributions. Methods. We computed and analysed global 3D ideal magnetohydrynamic (MHD) simulations of an accretion disk threaded by a large-scale magnetic field. We measured the turbulent state of the system by Reynolds averaging the ideal MHD equations and evaluate the role of the turbulent terms in the equilibrium of the system. We then computed the transport of mass, angular momentum, and magnetic fields in the disk to characterise its secular evolution. Finally, we performed a parameter exploration survey in order to characterise how the transport properties depend on the disk properties. Results. We find that weakly magnetised disks drive jets that carry a small fraction of the disk angular momentum away. The mass-weighted accretion speed remains subsonic, although there is always an upper turbulent atmospheric region where transsonic accretion takes place. We show that this turbulence is driven by a strongly magnetised version of the magneto-rotational instability. The internal disk structure therefore appears drastically different from the conventional hydrostatic picture. We expect that the turbulent atmosphere region will lead to non-thermal features in the emission spectra from compact objects. In addition, we show that the disk is subject to a secular viscous-type instability, which leads to the formation of long-lived ring-like structures in the disk surface density distribution. This instability is likely connected to the magnetic field transport. Finally, we show that for all of the parameters explored, the ambient magnetic field is always dragged inward in the disk at a velocity which increases with the disk magnetisation. Beyond a threshold on the latter, the disk undergoes a profound radial readjustment. It leads to the formation of an inner accretion-ejection region with a supersonic mass-weighted accretion speed and where the magnetic field distribution becomes steady and reaches a magnitude near equipartition with the thermal pressure. This inner structure shares many properties with the jet emitting disk model. Overall, these results pave the way for quantitative self-consistent secular disk models.

Stability of rotating scalar boson stars with nonlinear interactions

We study the stability of rotating scalar boson stars, comparing those made from a simple massive complex scalar (referred to as mini boson stars), to those with several different types of nonlinear interactions. To that end, we numerically evolve the nonlinear Einstein-Klein-Gordon equations in 3D, beginning with stationary boson star solutions. We show that the linear, non-axisymmetric instability found in mini boson stars with azimuthal number $m=1$ persists across the entire parameter space for these stars, though the timescale diverges in the Newtonian limit. Therefore, any boson star with $m=1$ that is sufficiently far into the non-relativistic regime, where the leading order mass term dominates, will be unstable, independent of the nonlinear scalar self-interactions. However, we do find regions of $m=1$ boson star parameter space where adding nonlinear interactions to the scalar potential quenches the non-axisymmetric instability, both on the non-relativistic, and the relativistic branches of solutions. We also consider select boson stars with $m=2$, finding instability in all cases. For the cases exhibiting instability, we follow the nonlinear development, finding a range of dynamics including fragmentation into multiple unbound non-rotating stars, and formation of binary black holes. Finally, we comment on the relationship between stability and criteria based on the rotating boson star's frequency in relation to that of a spherical boson star or the existence of a co-rotation point. The boson stars that we find not to exhibit instability when evolved for many dynamical times include rapidly rotating cases where the compactness is comparable to that of a black hole or neutron star.

Continuous time limit of the DTQW in 2D+1 and plasticity

A Plastic quantum walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in Di Molfetta and Arrighi (Quant Inf Process 19(2): 47, 2020), leading to a general quantum simulation scheme for simulating fermions in the relativistic and non-relativistic regimes. The extension to two physical dimensions is still missing and here, as a novel result, we demonstrate necessary and sufficient conditions concerning which discrete time quantum walks can admit plasticity, showing the resulting Hamiltonians. We consider coin operators as general 4 parameter unitary matrices, with parameters which are functions of the lattice step size $$\varepsilon $$ . This dependence on $$\varepsilon $$ encapsulates all functions of $$\varepsilon $$ for which a Taylor series expansion in $$\varepsilon $$ is well defined, making our results very general.

1000 Days of the Lowest-frequency Emission from the Low-luminosity GRB 171205A

Abstract We report the lowest-frequency measurements of gamma-ray burst (GRB) 171205A with the upgraded Giant Metrewave Radio Telescope (uGMRT) covering a frequency range of 250–1450 MHz and a period of 4–937 days. It is the first GRB afterglow detected in the 250–500 MHz frequency range and the second brightest GRB detected with the uGMRT. Even though the GRB was observed for nearly 1000 days, there is no evidence of a transition to a nonrelativistic regime. We also analyzed the archival Chandra X-ray data on day ∼70 and day ∼200. We also found no evidence of a jet break from the analysis of combined data. We fit synchrotron afterglow emission arising from a relativistic, isotropic, self-similar deceleration as well as from a shock breakout of a wide-angle cocoon. Our data also allowed us to discern the nature and the density of the circumburst medium. We found that the density profile deviates from a standard constant density medium and suggests that the GRB exploded in a stratified wind-like medium. Our analysis shows that the lowest-frequency measurements covering the absorbed part of the light curves are critical to unraveling the GRB environment. Our data combined with other published measurements indicate that the radio afterglow has a contribution from two components: a weak, possibly slightly off-axis jet and a surrounding wider cocoon, consistent with the results of Izzo et al. The cocoon emission likely dominates at early epochs, whereas the jet starts to dominate at later epochs, resulting in flatter radio light curves.

Black hole binaries and light fields: Gravitational molecules

We show that light scalars can form quasibound states around binaries. In the nonrelativistic regime, these states are formally described by the quantum-mechanical Schr\"odinger equation for a one-electron heteronuclear diatomic molecule. We performed extensive numerical simulations of scalar fields around black hole binaries, showing that a scalar structure condenses around the binary---we dub these states ``gravitational molecules.'' We further show that these are well described by the perturbative, nonrelativistic description.

Approximate solutions of D-dimensional Klein–Gordon equation with Yukawa potential via Nikiforov–Uvarov method

In this work, we obtain the Klein–Gordon equation solutions for the Yukawa potential using the Nikiforov–Uvarov method. The energy eigenvalues are obtained both in relativistic and non-relativistic regime. The corresponding eigenfunction are obtained in terms of Laguerre polynomial. We applied the present results to calculate heavy-meson masses of charmonium $$ c\bar{c} $$ and bottomonium $$ b\bar{b} $$ , and we got the numerical values for states 1S–1F. The results are in good agreement with experimental data and the work of other researchers.

Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential

Super-resolution of the Lie-Trotter splitting ($S_1$) and Strang splitting ($S_2$) is rigorously analyzed for the nonlinear Dirac equation without external magnetic potentials in the nonrelativistic regime with a small parameter $0<\varepsilon\leq 1$ inversely proportional to the speed of light. In this regime, the solution highly oscillates in time with wavelength at $O(\varepsilon^2)$. The splitting methods surprisingly show super-resolution, i.e. the methods can capture the solution accurately even if the time step size $\tau$ is much larger than the sampled wavelength at $O(\varepsilon^2)$. Similar to the linear case, $S_1$ and $S_2$ both exhibit $1/2$ order convergence uniformly with respect to $\varepsilon$. Moreover, if $\tau$ is non-resonant, i.e. $\tau$ is away from certain region determined by $\varepsilon$, $S_1$ would yield an improved uniform first order $O(\tau)$ error bound, while $S_2$ would give improved uniform $3/2$ order convergence. Numerical results are reported to confirm these rigorous results. Furthermore, we note that super-resolution is still valid for higher order splitting methods.

Analytical Solutions of the Schrödinger Equation with Kratzer-screened Coulomb Potential for a Quarkonium System

In this work, we obtain the Schrödinger equation solutions for the Kratzer potential plus screened Coulomb potential model using the series expansion method. The energy eigenvalues is obtained in non-relativistic regime and the corresponding unnormalized eigen function. Three special cases were obtained. We applied the present results to calculate heavy-meson masses of charmonium and bottomonium , and we got the numerical values for1S, 2S, 1P,2P, 3S, 4S,1D,2D and 1F states. The results are in good agreement with experimental data and the work of other researchers.

P-wave two-particle bound and scattering states in a finite volume including QED

The mass shifts for two-fermion bound and scattering P-wave states subject to the long-range interactions due to QED in the non-relativistic regime are derived. Introducing a short range force coupling the spinless fermions to one unit of angular momentum in the framework of pionless EFT, we first calculate both perturbatively and non-perturbatively the Coulomb corrections to fermion–fermion scattering in the continuum and infinite volume context. Motivated by the research on particle–antiparticle bound states, we extend the results to fermions of identical mass and opposite charge. Second, we transpose the system onto a cubic box with periodic boundary conditions and we calculate the finite volume corrections to the energy of the lowest bound and unbound T_1^{-} eigenstates. In particular, power law corrections proportional to the fine structure constant and resembling the recent results for S-wave states are found. Higher order contributions in alpha are neglected, since the gapped nature of the momentum operator in the finite-volume environnement allows for a perturbative treatment of the QED interactions.

Apparent superluminal velocities and random walk in the velocity space

We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of diffusion in the velocity space are demonstrated in both non-relativistic and relativistic regimes.