Relativistic Modes Research Articles

Weyl fermions in a (2+1)-dimensional gravitational wave spacetime

In this study, we work on understanding the behavior of relativistic fermions within the framework of a (2+1)-dimensional gravitational wave environment. Our main objective is to uncover an analytical solution for the massless Dirac equation in this particular scenario. Initially, we derive a set of coupled equations that describe the quantum dynamics of the system under consideration. Subsequently, we embark on finding an analytical solution for the resulting wave equation governing Weyl fermions by utilizing the generators associated with the [Formula: see text] algebra. This approach enables us to determine the relativistic frequency modes of the system. We then delve into examining how the parameters of the gravitational wave spacetime influence the real oscillation modes of Weyl fermions. Our findings highlight the sensitivity of Weyl fermions to the specific gravitational wave spacetime background being considered.

Real and damped modes for an interacting fermion–antifermion pair: exciton in monolayer medium

In this manuscript, we investigate the interaction between a fermion–antifermion pair in (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-dimensions, governed by a Coulomb-type inter-particle potential. We explore analytical solutions for a fully covariant two-body Dirac equation derived from quantum electrodynamics, focusing on a spinless composite system. We present a non-perturbative second-order wave equation and derive a solution using the generators of the sℓ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s\\ell _{2}$$\\end{document} algebra. Subsequently, we determine the relativistic frequency modes of the system and extend our findings to electron–hole pairs in a monolayer medium in the vicinity of substrate. We analyze the impact of the effective dielectric constant (ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon$$\\end{document}) of the surrounding medium on the real and damped modes of an exciton. Our results indicate that the ground state binding energy of the system can vary from the order of eV to a few meV, depending on changes in ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon$$\\end{document}. Additionally, we observe that the decay time for the ground state of such an exciton is on the order of ∼10-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 10^{-12}$$\\end{document} s. These findings suggest that the evolution of such a pair can be controlled by adjusting the effective dielectric constant of the surrounding medium.

Dirac exciton-polariton condensates in photonic crystal gratings.

Bound states in the continuum have recently been utilized in photonic crystal gratings to achieve strong coupling and ultralow threshold condensation of exciton-polariton quasiparticles with atypical Dirac-like features in their dispersion relation. Here, we develop the single- and many-body theory of these new effective relativistic polaritonic modes and describe their mean-field condensation dynamics facilitated by the interplay between protection from the radiative continuum and negative-mass optical trapping. Our theory accounts for tunable grating parameters giving full control over the diffractive coupling properties between guided polaritons and the radiative continuum, unexplored for polariton condensates. In particular, we discover stable cyclical condensate solutions mimicking a driven-dissipative analog of the zitterbewegung effect characterized by coherent superposition of ballistic and trapped polariton waves. We clarify important distinctions between the polariton nearfield and farfield explaining recent experiments on the emission characteristics of these long lived nonlinear Dirac polaritons.

Evolution of an interacting fermion–antifermion pair in the near-horizon of the BTZ black hole

In this study, we investigate the evolution of a composite system comprising a fermion–antifermion pair engaged in Cornell-type non-minimal interaction in the near-horizon region of a BTZ black hole. Our exploration involves the derivation of an exact solution for the covariant two-body Dirac equation, derived from quantum electrodynamics through the action principle. To commence our analysis, we formulate the relevant equation, resulting in a 4×4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\ imes 4$$\\end{document} dimensional matrix equation that governs the relative motion of the fermion–antifermion pair. Notably, we demonstrate that this matrix equation results in an exactly solvable wave equation, enabling us to determine the relativistic frequency modes for this spinless static composite system. Our findings unveil a temporal decay in these modes, with the decay time explicitly dependent on both the inter-particle interaction and the spacetime parameters. Our comprehensive examination extends to a detailed analysis of the system’s evolution, shedding light on the influence of inter-particle interaction on the evolution of a fermion–antifermion pair in the near-horizon region of the BTZ black hole.

POST-POSTMODERN CHANGE OF SENSIBILITY IN PAUL AUSTER’S SUNSET PARK

At the turn of the millennium, the young writers of the New Sincerity movement tried to create a new realist literature by getting rid of the destructive power of postmodern irony. The consecrated writers of the old postmodern guard, whose Weltanschauung was conformed to the style and the relativistic reality-processing modes of the previous paradigm, saw this change with scepticism. Nevertheless, there was a change in their sensibility when approaching certain themes. This article analyses Paul Auster’s Sunset Park as paradigmatic example of that shift in order to shed some light on its nature.

Stellar basins of gravitationally bound particles

A new physical phenomenon is identified: volumetric stellar emission into gravitationally bound orbits of weakly coupled particles such as axions, moduli, hidden photons, and neutrinos. While only a tiny fraction of the instantaneous luminosity of a star (the vast majority of the emission is into relativistic modes), the continual injection of these particles into a small part of phase space causes them to accumulate over astrophysically long time scales, forming what I call a "stellar basin", in analogy with the geologic kind. The energy density of the Solar basin will surpass that of the relativistic Solar flux at Earth's location after only a million years, for any sufficiently long-lived particle produced through an emission process whose matrix elements are unsuppressed at low momentum. This observation has immediate and striking consequences for direct detection experiments---including new limits on axion parameter space independent of dark matter assumptions---and may also increase the prospects for indirect detection of weakly interacting particles around compact stars.

Thermal radiation equilibrium: (nonrelativistic) classical mechanics versus (relativistic) classical electrodynamics

Physics students continue to be taught the erroneous idea that classical physics leads inevitably to energy equipartition, and hence to the Rayleigh–Jeans law for thermal radiation equilibrium. Actually, energy equipartition is appropriate only for nonrelativistic classical mechanics, but has only limited relevance for a relativistic theory such as classical electrodynamics. In this article, we discuss harmonic-oscillator thermal equilibrium from three different perspectives. First, we contrast the thermal equilibrium of nonrelativistic mechanical oscillators (where point collisions are allowed and frequency is irrelevant) with the equilibrium of relativistic radiation modes (where frequency is crucial). The Rayleigh–Jeans law appears from applying a dipole-radiation approximation to impose the nonrelativistic mechanical equilibrium on the radiation spectrum. In this discussion, we note the possibility of zero-point energy for relativistic radiation, which possibility does not arise for nonrelativistic classical-mechanical systems. Second, we turn to a simple electromagnetic model of a harmonic oscillator and show that the oscillator is fully in radiation equilibrium (which involves all radiation multipoles, dipole, quadrupole, etc) with classical electromagnetic zero-point radiation, but is not in equilibrium with the Rayleigh–Jeans spectrum. Finally, we discuss the contrast between the flexibility of nonrelativistic mechanics with its arbitrary potential functions allowing separate scalings for length, time, and energy, with the sharply-controlled behavior of relativistic classical electrodynamics with its single scaling connecting together the scales for length, time, and energy. It is emphasized that within classical physics, energy-sharing, velocity-dependent damping is associated with the low-frequency, nonrelativistic part of the Planck thermal radiation spectrum, whereas acceleration-dependent radiation damping is associated with the high-frequency adiabatically-invariant and Lorentz-invariant part of the spectrum corresponding to zero-point radiation.

Dynamics of the generalized unimodular gravity theory

The Hamiltonian formalism of the generalized unimodular gravity theory, which was recently suggested as a model of dark energy, is shown to be a complicated example of constrained dynamical system. The set of its canonical constraints has a bifurcation -- splitting of the theory into two branches differing by the number and type of these constraints, one of the branches effectively describing a gravitating perfect fluid with the time-dependent equation of state, which can potentially play the role of dark energy in cosmology. The first class constraints in this branch generate local gauge symmetries of the Lagrangian action -- two spatial diffeomorphisms -- and rule out the temporal diffeomorphism which does not have a realization in the form of the canonical transformation on phase space of the theory and turns out to be either nonlocal in time or violating boundary conditions at spatial infinity. As a consequence, the Hamiltonian reduction of the model enlarges its physical sector from two general relativistic modes to three degrees of freedom including the scalar graviton. This scalar mode is free from ghost and gradient instabilities on the Friedmann background in a wide class of models subject to a certain restriction on time-dependent parameter $w$ of the dark fluid equation of state, $p=w\varepsilon$. For a special family of models this scalar mode can be ruled out even below the phantom divide line $w=-1$, but this line cannot be crossed in the course of the cosmological expansion. This is likely to disable the generalized unimodular gravity as a model of the phenomenologically consistent dark energy scenario, but opens the prospects in inflation theory with a scalar graviton playing the role of inflaton.

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

New structures of power density spectra for four Kepler active galactic nuclei

Many nearby AGNs display a significant short-term variability. In this work we re-analyze photometric data of four active galactic nuclei observed by Kepler in order to study the flickering activity, having as main goal that of searching for multiple components in the power density spectra. We find that all four objects have similar characteristics, with two break frequencies at approximately log(f/Hz)=-5.2 and -4.7. We consider some physical phenomena whose characteristic time-scales are consistent with those observed, in particular mass accretion fluctuations in the inner geometrically thick disc (hot X-ray corona) and unstable relativistic Rayleigh-Taylor modes. The former is supported by detection of the same break frequencies in the Swift X-ray data of ZW229-15. We also discuss rms-flux relations, and we detect a possible typical linear trend at lower flux levels. Our findings support the hypothesis of a multiplicative character of variability, in agreement with the propagating accretion fluctuation model.

Tartarus: A relativistic Green’s function quantum average atom code

A relativistic Green’s Function quantum average atom model is implemented in the Tartarus code for the calculation of equation of state data in dense plasmas. We first present the relativistic extension of the quantum Green’s Function average atom model described by Starrett [1]. The Green’s Function approach addresses the numerical challenges arising from resonances in the continuum density of states without the need for resonance tracking algorithms or adaptive meshes, though there are still numerical challenges inherent to this algorithm. We discuss how these challenges are addressed in the Tartarus algorithm. The outputs of the calculation are shown in comparison to PIMC/DFT-MD simulations of the Principal Shock Hugoniot in Silicon. We also present the calculation of the Hugoniot for Silver coming from both the relativistic and nonrelativistic modes of the Tartarus code.

Topological Quantum Phase Transition and Local Topological Order in a Strongly Interacting Light-Matter System

An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system. We study this system, in a one dimensional array of nonlinear cavities. Topological quantum phase transition occurs with massless excitation only for the finite detuning process. We present a few results based on the exact analytical calculations along with the physical explanations. We observe the emergence of massive Majorana fermion mode at the topological state, massless Majorana-Weyl fermion mode during the topological quantum phase transition and Dirac fermion mode for the non-topological state. Finally, we study the quantized Berry phase (topological order) and its connection to the topological number (winding number).

Anisotropies of gravitational wave backgrounds: A line of sight approach

In the weak field regime, gravitational waves can be considered as being made up of collisionless, relativistic tensor modes that travel along null geodesics of the perturbed background metric. We work in this geometric optics picture to calculate the anisotropies in gravitational wave backgrounds resulting from astrophysical and cosmological sources. Our formalism yields expressions for the angular power spectrum of the anisotropies. We show how the anisotropies are sourced by intrinsic, Doppler, Sachs–Wolfe, and Integrated Sachs–Wolfe terms in analogy with Cosmic Microwave Background photons.

On longevity of I-ball/oscillon

We study I-balls/oscillons, which are long-lived, quasi-periodic, and spatially localized solutions in real scalar field theories. Contrary to the case of Q-balls, there is no evident conserved charge that stabilizes the localized configuration. Nevertheless, in many classical numerical simulations, it has been shown that they are extremely long-lived. In this paper, we clarify the reason for the longevity, and show how the exponential separation of time scales emerges dynamically. Those solutions are time-periodic with a typical frequency of a mass scale of a scalar field. This observation implies that they can be understood by the effective theory after integrating out relativistic modes. We find that the resulting effective theory has an approximate global U(1) symmetry reflecting an approximate number conservation in the non-relativistic regime. As a result, the profile of those solutions is obtained via the bounce method, just like Q-balls, as long as the breaking of the U(1) symmetry is small enough. We then discuss the decay processes of the I-ball/oscillon by the breaking of the U(1) symmetry, namely the production of relativistic modes via number violating processes. We show that the imaginary part is exponentially suppressed, which explains the extraordinary longevity of I-ball/oscillon. In addition, we find that there are some attractor behaviors during the evolution of I-ball/oscillon that further enhance the lifetime. The validity of our effective theory is confirmed by classical numerical simulations. Our formalism may also be useful to study condensates of ultra light bosonic dark matter, such as fuzzy dark matter, and axion stars, for instance.

Tests of General Relativity with GW150914.

The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (postinspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following the peak of GW150914 are consistent with the least-damped quasinormal mode inferred from the mass and spin of the remnant black hole. By using waveform models that allow for parametrized general-relativity violations during the inspiral and merger phases, we perform quantitative tests on the gravitational-wave phase in the dynamical regime and we determine the first empirical bounds on several high-order post-Newtonian coefficients. We constrain the graviton Compton wavelength, assuming that gravitons are dispersed in vacuum in the same way as particles with mass, obtaining a 90%-confidence lower bound of 10^{13} km. In conclusion, within our statistical uncertainties, we find no evidence for violations of general relativity in the genuinely strong-field regime of gravity.

Interpolating relativistic and nonrelativistic Nambu-Goldstone and Higgs modes

When a continuous symmetry is spontaneously broken in non-relativistic theories, there appear Nambu-Goldstone (NG) modes, whose dispersion relations are either linear (type-I) or quadratic (type-II). We give a general framework to interpolate between relativistic and non-relativistic NG modes, revealing a nature of type-I and II NG modes in non-relativistic theories. The interpolating Lagrangians have the nonlinear Lorentz invariance which reduces to the Galilei or Schrodinger invariance in the non-relativistic limit. We find that type-I and type-II NG modes in the interpolating region are accompanied with a Higgs mode and a chiral NG partner, respectively, both of which are gapful. In the ultra-relativistic limit, a set of a type-I NG mode and its Higgs partner remains, while a set of type-II NG mode and gapful NG partner turns to a set of two type-I NG modes. In the non-relativistic limit, the both types of accompanied gapful modes become infinitely massive, disappearing from the spectrum. The examples contain a phonon in Bose-Einstein condensates, a magnon in ferromagnets, and a Kelvon and dilaton-magnon localized around a skyrmion line in ferromagnets.

On the relativistic nature of predicted and real physical experiences: A field experiment

ObjectivesAn important yet unresolved question stemming from judgment and decision-making literature is whether individuals evaluate physical experiences in relative or absolute terms. Design and methodThe study examined 181 experienced basketball players in a 2 (type of experience: predicted versus real) × 2 (evaluation mode: separate versus joint) × 2 (type of activity: running versus shooting) experimental research design. ResultsWe demonstrated that individuals who were familiar with physical tasks evaluated predicted and real physical experiences in absolute terms. In addition, we showed that relativistic modes of evaluation applied to real physical experiences but not predicted physical experiences. ConclusionsThis research contributes to the debate concerning whether prior task experience influences formation of relative evaluations, and reveals that contexts that urge for relative evaluations undermine happiness with physical tasks.

Epistemic Beliefs about Justification Employed by Physics Students and Faculty in Two Different Problem Contexts

This study examines the epistemic beliefs about justification employed by physics undergraduate and graduate students and faculty in the context of solving a standard classical physics problem and a frontier physics problem. Data were collected by a think-aloud problem solving session followed by a semi-structured interview conducted with 50 participants, 10 participants at freshmen, seniors, masters, PhD, and faculty levels. Seven modes of justification were identified and used for exploring the relationships between each justification mode and problem context, and expertise level. The data showed that justification modes were not mutually exclusive and many respondents combined different modes in their responses in both problem contexts. Success on solving the standard classical physics problem was not related to any of the justification modes and was independent of expertise level. The strength of the association across the problem contexts for the authoritative, rational, and empirical justification modes fell in the medium range and for the modeling justification mode fell in the large range of practical significance. Expertise level was not related with the empirical and religious justification modes. The strength of the association between the expertise level and the authoritative, rational, experiential, and relativistic justification modes fell in the medium range, and the modeling justification mode fell in the large range of practical significance. The results provide support for the importance of context for the epistemic beliefs about justification and are discussed in terms of the implications for teaching and learning science.

Effects of wiggler and axial guide fields on the relativistic high-frequency waves in a cylindrical plasma waveguide

An analysis of the azimuthally symmetrical, high frequency eigenmodes of a cylindrical metallic waveguide completely filled with a one-dimensional helical wiggler and relativistic magnetized plasma is presented. A relativistic nonlinear wave equation is derived in a form including the coupling of EH and HE modes due to the finite axial and wiggler magnetic fields. This treatment shows that the dispersion curves are dependent on dγ∕dt and Bw, ignored in previous works. The difference between relativistic modes with effects of wiggler field and nonrelativistic cases is shown. This study is benefiting to improve the devices for generation of high-power electromagnetic radiation, charged particle acceleration, and other applications of plasma waveguide.

Damped Bernstein modes in a weakly relativistic pair plasma

Relativistic Bernstein modes are not totally undamped, but have a small, negative definite imaginary frequency component that peaks where the frequency is closest to the rest cyclotron harmonic.