The spectral line asymmetry of the Doppler effect in relativistic plasmas

{In this work, we present a comparative study between the relativistic and non- relativistic Doppler effects on spectral line profiles in ultra-hot plasmas at the laboratory system. We have established an exact formula of the relativistic Doppler profile in ultra-high-temperature plasma that is not a Gaussian one (unlike the nonrelativistic Doppler profile that is Gaussian). We have also derived a new FWHM (Full Width at Half Maximum) formula of the corresponding profile that is different from the non-relativistic FWHM (sqrtlog(T=M)). We have also shown that, in the relativistic case, Doppler broadening exhibits an asymmetry of spectral line profile (non- gaussian profile). To ensure the validity of our investigation, we have compared our theoretical calculation with the experimental results that shows a good agreement.

Contact interactions II; Gross-Pitaewskii equation, Bose-Einstein condensate, Fermi sea

In Dell’Antonio (Eur Phys J Plus 13:1–20, 2021), we explored the possibility to analyse contact interaction in Quantum Mechanics using a variational tool, Gamma Convergence. Here, we extend the analysis in Dell’Antonio (Eur Phys J Plus 13:1–20, 2021) of joint weak contact of three particles to the non-relativistic case in which the free one particle Hamiltonian is $$ H_0 = - \frac{\Delta }{2M} $$ H 0 = - Δ 2 M . We derive the Gross–Pitaevskii equation for a system of three particles in joint weak contact. We then define and study strong contact and show that the Gross–Pitaevskii equation is also the variational equation for the energy of the Bose–Einstein condensate (strong contact in a four-particle system). We add some comments on Bogoliubov’s theory. In the second part, we use the non-relativistic Pauli equation and weak contact to derive the spectrum of the conduction electrons in an infinite crystal. We prove that the spectrum is pure point with multiplicity two and eigenvalues that scale as $$ \frac{1}{log {n}}$$ 1 logn .

The general-relativistic case for super-substantivalism

Super-substantivalism (of the type we’ll consider) roughly comprises two core tenets: (1) the physical properties which we attribute to matter (e.g. charge or mass) can be attributed to spacetime directly, with no need for matter as an extraneous carrier “on top of” spacetime; (2) spacetime is more fundamental than (ontologically prior to) matter. In the present paper, we revisit a recent argument in favour of super-substantivalism, based on General Relativity. A critique is offered that highlights the difference between (various accounts of) fundamentality and (various forms of) ontological dependence. This affords a metaphysically more perspicuous view of what super-substantivalism’s tenets actually assert, and how it may be defended. We tentatively propose a re-formulation of the original argument that not only seems to apply to all classical physics, but also chimes with a standard interpretation of spacetime theories in the philosophy of physics.

Entanglement entropy with Lifshitz fermions

We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent z. Remarkably, in the ground state the entanglement entropy vanishes for even values of z, whereas for odd values it is independent of z and equal to the relativistic case with z=1. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of z and T which we plot using the lattice correlation method. The dependence on the even- or oddness of z still shows for small temperatures, but is washed out for large temperatures or large values of z.

On the reformulation of the Thomas–Fermi model to make it compatible with the Planck-scale

Thomas–Fermi model is considered here to make it cogent to capture the Planck-scale effect with the use of a generalization of uncertainty relation. Here generalization contains both linear and quadratic terms of momentum. We first reformulate the Thomas–Fermi model for the non-relativistic case. We have shown that it can also be reformulated for taking into account the relativistic effect. We study the dialectic screening for both the non-relativistic and relativistic cases and find out the Fermi length for both the cases explicitly.

Relativistic Corrections to Phase Shift Calculation in the GNXAS Package

Modern XAFS (X-ray Absorption Fine Structure) data-analysis is based on accurate multiple-scattering (MS) calculations of the x-ray absorption cross-section. In this paper, we present the inclusion and test of relativistic corrections for the multiple-scattering calculations within the GnXAS suite of programs, which is relevant to the treatment of the XAFS signals when atoms with high atomic number are contained into the system. We present a suitable strategy for introducing relativistic corrections without altering the basic structure of the programs. In particular, this is realized by modifying only the Phagen program calculating the atomic absorption cross sections and scattering t-matrices for the selected cluster. The modification incorporates a pseudo-Schrödinger Equation (SE) replacing the Dirac relativistic form. The phase-shift calculations have been put to a test in two known molecular and crystalline cases: molecular bromine Br2 and crystalline Pb. Calculations in an extended energy range have been shown to be very close to the non-relativistic case for Br2 (Br K-edge) while corrections have been found to exceed 25% for amplitude and phases of the XAFS multiple-scattering signals (Pb L3-edge). Benefits in the structural refinement using relativistic corrections are discussed for crystalline Pb at room temperature.

High precision methods for solving a system of cold plasma equations taking into account electron–ion collisions

High precision simulation algorithms are proposed and justified for modelling cold plasma oscillations taking into account electron–ion collisions in the non-relativistic case. The specific feature of the approach is the use of Lagrangian variables for approximate solution of the problem formulated initially in Eulerian variables. High accuracy is achieved both through the use of analytical solutions on trajectories of particles and due to sufficient smoothness of the solution in numerical integration of Cauchy problems. Numerical experiments clearly illustrate the obtained theoretical results. As a practical application, a simulation of the well-known breaking effect of multi-period relativistic oscillations is carried out. It is shown that with an increase in the collision coefficient one can observe that the breaking process slows down until it is completely eliminated.

Radiation instability of a relativistic electron beam moving in a split resonator

In this paper, we considered the radiation instability in a split asymmetric resonator for the relativistic case assuming the space charge of the beam. In the small-signal approximation, expressions for the energy loss by a particle passing through the resonator and for the beam current modulation are obtained. Based on analytical and numerical calculations, it is shown that the symmetric configuration provides the highest growth rate of instability. It is found that with the increase of the initial electron energy, the modulation of the beam current as well as the efficiency of the energy transfer from particles to the electromagnetic field decrease. The increase of the beam density has a positive effect on the radiation instability. The results obtained have to be taken into account when developing generators of electromagnetic radiation or a system for modulating the beam current based on a split resonator.

Geometrizing non-relativistic bilinear deformations

We define three fundamental solvable bilinear deformations for any massive non-relativistic 2d quantum field theory (QFT). They include the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformation and the recently introduced hard rod deformation. We show that all three deformations can be interpreted as coupling the non-relativistic QFT to a specific Newton-Cartan geometry, similar to the Jackiw-Teitelboim-like gravity in the relativistic case. Using the gravity formulations, we derive closed-form deformed classical Lagrangians of the Schrödinger model with a generic potential. We also extend the dynamical change of coordinate interpretation to the non-relativistic case for all three deformations. The dynamical coordinates are then used to derive the deformed classical Lagrangians and deformed quantum S-matrices.

Bowen–York model solution redux

Initial value problem in general relativity is often solved numerically; with only a few exceptions one of which is the “model” solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between [0, 0.592). This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is 59.2% of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.