Relativistic Behavior Research Articles

Thermodynamic properties of an interacting fermion-antifermion pair in a magnetized spacetime with a non-zero cosmological constant

In a magnetized three-dimensional Bonnor-Melvin spacetime with a non-zero cosmological constant, we explore the dynamics of a fermion-antifermion pair interacting through an attractive Coulomb potential. To analyze the relativistic behavior, we seek an analytical solution for the fully covariant two-body Dirac equation derived from quantum electrodynamics. The resulting equation provides a second-order wave equation that governs the relative motion of the interacting pair. Obtaining an exact solution to this wave equation seems not possible; however, we notice solubility, especially when we consider particles to be closely spaced, meaning as the distance between them approaches zero. At that rate, we determine the energy eigenvalues and wave functions utilizing well-known special functions. By employing these solutions, we determine the thermal properties of this system. Despite the divergence observed in the partition function, we effectively tackle this issue by applying a regularization technique based on the mathematical zeta Hurwitz function. This method facilitates the computation of various thermal quantities, such as free energy, total energy, entropy function, and specific heat. Consequently, we provide an in-depth analysis of the thermodynamic characteristics of the system under consideration.

Nanoscale mapping of relativistic photocarrier transports in epitaxial graphene surface and edge states

We report the direct mapping of photo-transport properties of relativistic carriers generated on terrace-surface and terrace-edge structures of epitaxial graphene grown on silicon carbide. In this method, a conductive probe made a direct contact with epitaxial graphene and scanned the surface, allowing us to map the topography, current, and noise of graphene with nanoscale resolutions via a scanning noise microscopy. The maps were further analyzed by a two-dimensional network model to obtain the sheet-conductance (S□) and noise-source density (neff) distributions of epitaxial graphene. The topography image showed the formation of terraces, which could be attributed to the different decomposition rate of silicon atoms during the graphene growth. The terraces of graphene exhibited uniform S□, being separated by one-dimensional terrace-edges. Interestingly, terrace-edges exhibited a rather large neff with a power-law relationship of S□ ∝ neff−0.5, indicating a typical hopping conduction. However, in terrace-surfaces, sheet-conductance was nearly independent on neff, which was attributed to the relativistic nature of charge carriers unaffected by charge-trapping potential. Notably, under illumination, we observed the relativistic behavior of photocarriers in overall graphene terraces, presumably because photocarriers were generated through charge-transfer complexes formation at epitaxial graphene/substrate interface without the participation of noise-sources. Interestingly, we observed nearly homogeneous photoconductance and neff, which could be possibly due to the merger of one-dimensional edge-states into two-dimensional surface-states. The mapping of photoconductance and photo-traps provides valuable insights into the generation of relativistic photocarriers in epitaxial graphene.

Introducing the Framework of a "Dynamic" Higher Dimensional Spacetime. How Time Behaves in it. Similarities with Quantum Mechanical and Relativistic Behavior

Introducing the Framework of a "Dynamic" Higher Dimensional Spacetime. How Time Behaves in it. Similarities with Quantum Mechanical and Relativistic Behavior

Relativistic potential energy of a non-dissipative classical harmonic oscillator

The well-known relation of Einstein's relativistic energy E=mc2 for a free particle is extended to cover the total relativistic energy of a classical harmonic oscillator (CHO) by calculating the relativistic potential energy. This study is essentially concerned with the relativistic mass m=γm0, where the Lorentz factor γ transforms the state of the second-order differential equation of a CHO from linear into nonlinear. Although the nonlinear solution still remains periodic, the amplitude A(β) and angular frequency ω(β) are determined only by the dimensionless factor β=X˙(0)/c (the ratio of the initial velocity X˙(0) to the light speed c). It is demonstrated that the time period T(β) and Hook force respectively tend to infinity and zero when β→1 so that the state of the bound particle approaches that of a free particle. By contrast, the relativistic behavior of a quantum harmonic oscillator (QHO) in subatomic scales, such as the relativistic ro-vibrational motion of an electron in circular Bohr orbits, is completely different. The relativistic model of Bohr atom is discussed in detail by using the relativistic relations of a CHO according to the Ehrenfest theorem. Finally, the results are confirmed by demonstrating energy conservation.

A charged particle must be treated relativistically in classical theory

A charged particle which is allowed to accelerate must have relativistic behavior because it is coupled to electromagnetic radiation which propagates at the speed of light. We treat the simple steady-state situation of a charged particle moving in a circular orbit with counter-propagating plane waves providing the power which balances the energy radiated away by the accelerating charge. It is emphasized that only an electromagnetic arrangement, such as a Coulomb potential or a constant magnetic field, can provide the relativistic central force for the particle motion.

Enhanced Magnon Spin Current Using the Bosonic Klein Paradox

Efficient manipulation of magnons for information processing is a central topic in spintronics and magnonics. An outstanding challenge for long-distance spin transport with minimal dissipation is to overcome the relaxation of magnons and to amplify the spin current they carry. Here, we propose to amplify magnon currents based on the realization of the bosonic Klein paradox in magnetic nanostructures. This paradox involves the antimagnon, carrying opposite spin and energy, the existence of which is usually precluded by ferromagnetic instabilities, as it is an excitation at negative energy. We show that by appropriately tuning the effective dissipation through spin-orbit torques, both magnons and antimagnons are dynamically stabilized. As a result, we find that the reflection coefficient of incident magnons at an interface between two coupled magnets can become larger than one, thereby amplifying the reflected magnon current. Our findings can lead to magnon amplifier devices for spintronic applications. Furthermore, our findings yield a solid-state platform to study the relativistic behavior of bosonic particles, which is an outstanding challenge with fundamental particles.

Cosmologically degenerate fermions

Dark matter (DM) with a mass below a few keV must have a phase space distribution that differs substantially from the Standard Model particle thermal phase space: otherwise, it will free stream out of cosmic structures as they form. We observe that fermionic DM $\ensuremath{\psi}$ in this mass range will have a non-negligible momentum in the early Universe, even in the total absence of thermal kinetic energy. This is because the fermions were inevitably more dense at higher redshifts, and thus experienced Pauli degeneracy pressure. They fill up the lowest-momentum states, such that a typical fermion gains a momentum $\ensuremath{\sim}\mathcal{O}({p}_{F})$ that can exceed its mass ${m}_{\ensuremath{\psi}}$. We find a simple relation between ${m}_{\ensuremath{\psi}}$, the current fraction ${f}_{\ensuremath{\psi}}$ of the cold DM energy density in light fermions, and the redshift at which they were relativistic. Considering the impacts of the transition between nonrelativistic and relativistic behavior as revealed by constraints on $\mathrm{\ensuremath{\Delta}}{N}_{\mathrm{eff}}$ and the matter power spectrum, we derive qualitatively new bounds in the ${f}_{\ensuremath{\psi}}\ensuremath{-}{m}_{\ensuremath{\psi}}$ plane. We also improve existing bounds for ${f}_{\ensuremath{\psi}}=1$ to be ${m}_{\ensuremath{\psi}}\ensuremath{\ge}2\text{ }\text{ }\mathrm{keV}$. We remark on implications for direct detection and suggest models of dark sectors that may give rise to cosmologically degenerate fermions.

Relativistic collapse of Landau levels of Kane fermions in crossed electric and magnetic fields

Using an elegant model involving only $\Gamma_{6c}$ and $\Gamma_{8v}$ bands, massless Kane fermions were defined as the particles associated with the peculiar band structure of gapless HgCdTe crystals. Although their dispersion relation resembles that of a pseudo-spin-1 Dirac semimetal, these particles were originally considered to be hybrids of pseudospin-1 and -1/2 fermions. Here we unequivocally find that by considering an additional $\Gamma_{7c}$ conduction band inherent in HgCdTe crystals, the Kane fermions are ultimately two nested Dirac particles. This observation allows the direct application of Lorentz transformations to describe the relativistic behavior of these particles in crossed electric and magnetic fields. By studying the relativistic collapse of their Landau levels at different orientations between the crossed fields and the main crystallographic axes, we demonstrate that the Kane fermions strikingly decay into two independent Dirac particles with increasing of electric field. Our results provide new insight into semi-relativistic effects in narrow-gap semiconductors in crossed electric and magnetic fields.

Dynamical chameleon neutron stars: Stability, radial oscillations, and scalar radiation in spherical symmetry

Scalar-tensor theories whose phenomenology differs significantly from general relativity on large (e.g. cosmological) scales do not typically pass local experimental tests (e.g. in the solar system) unless they present a suitable "screening mechanism". An example is provided by chameleon screening, whereby the local general relativistic behavior is recovered in high density environments, at least in weak-field and quasi-static configurations. Here, we test the validity of chameleon screening in strong-field and highly relativistic/dynamical conditions, by performing fully non-linear simulations of neutron stars subjected to initial perturbations that cause them to oscillate or even collapse to a black hole. We confirm that screened chameleon stars are stable to sufficiently small radial oscillations, but that the frequency spectrum of the latter shows deviations from the general relativistic predictions. We also calculate the scalar fluxes produced during collapse to a black hole, and comment on their detectability with future gravitational-wave interferometers.

Entanglement and quantum tomography with top quarks at the LHC

Entanglement is a central subject in quantum mechanics. Due to its genuine relativistic behavior and fundamental nature, high-energy colliders are attractive systems for the experimental study of fundamental aspects of quantum mechanics. We propose the detection of entanglement between the spins of top–antitop–quark pairs at the LHC, representing the first proposal of entanglement detection in a pair of quarks, and also the entanglement observation at the highest energy scale so far. We show that entanglement can be observed by direct measurement of the angular separation between the leptons arising from the decay of the top–antitop pair. The detection can be achieved with high statistical significance, using the current data recorded during Run 2 at the LHC. In addition, we develop a simple protocol for the quantum tomography of the top–antitop pair. This experimental technique reconstructs the quantum state of the system, providing a new experimental tool to test theoretical predictions. Our work explicitly implements canonical experimental techniques in quantum information in a two-qubit high-energy system, paving the way to use high-energy colliders to also study quantum information aspects.

Moire Is Different

Graphene, as the thinnest material ever found, exhibits unconventionally relativistic behaviour of Dirac fermions. However, unusual phenomena (such as superconductivity) arise when stacking two graphene layers and twisting the bilayer graphene. The relativistic Dirac fermion in graphene has been widely studied and understood, but the large change observed in twisted bilayer graphene (TBG) is intriguing and still unclear because only van der Waals force (vdW) interlayer interaction is added from graphene to TBG and such a very weak interaction is expected to play a negligible role. To understand such dramatic variation, we studied the electronic structures of monolayer, bilayer and twisted bilayer graphene. Twisted bilayer graphene creates different moiré patterns when turned at different angles. We proposed tight-binding and effective continuum models and thereby drafted a computer code to calculate their electronic structures. Our calculated results show that the electronic structure of twisted bilayer graphene changes significantly even by a tiny twist. When bilayer graphene is twisted at special “magic angles”, flat bands appear. We examined how these flat bands are created, their properties and the relevance to some unconventional physical property such as superconductivity. We conclude that in the nanoscopic scale, similar looking atomic structures can create vastly different electronic structures. Like how P. W. Anderson stated that similar looking fields in science can have differences in his article “More is Different”, similar moiré patterns in twisted bilayer graphene can produce different electronic structures.

Relativistic magnetic lensing of electron beams using superconducting spheres

In this paper, the theoretical design of magnetic electron lens made of macroscopic superconducting spheres in rotation is proposed. The relativistic quantum behavior of an electron in the magnetic field induced by rotating bulk superconductors is described based on the Dirac equation, and electron beam transport is manifested in specific cases. Based on this approach, the focal length of magnetic electron lens made of macroscopic superconductors is theoretically calculated. Subsequently, the characterization of relativistic electron beam manipulating capability of newly designed magnetic electron lens is carried out by variation of the system parameters. Owing to the ability to focus the relativistic electron beam in versatile and precise manner, this approach offers a new way to study a macroscopic system of superconductors based on special relativity, and it sets a milestone in the construction of a new generation of magnetic electron lenses with superconducting spheres. The model is inherited and developed based on previous calculations of the field induced by spherical and cylindrical superconductors (L.B. Holdeman, NASA TR R-443 (1975); R.G. Rystephanick, Can. J. Phys. 51 (1973) 789–794) and the quantum theory of electron propagation through an electron lens (R. Jagannathan, Phys. Rev. A 42 (1990) 6674).

Geometrization of Newtonian Dynamics

Riemann’s principle “force equals geometry” provided the basis for Einstein’s General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any conservative force. We introduce the relativity of spacetime : an object lives in its own spacetime, whose geometry is determined by all of the forces affecting it. We also introduce the Generalized Principle of Inertia which unifies Newton’s first and second laws and states that: An inanimate object moves freely, that is, with zero acceleration, in its own spacetime. We derive the metric of an object’s spacetime in two ways. The first way uses conservation of energy to derive a Newtonian metric. We reveal a physical deficiency of this metric (responsible for the inability of Newtonian dynamics to account for relativistic behavior), and remove it. The dynamics defined by the corrected Newtonian metric leads to a new Relativistic Newtonian Dynamics (RND) for both massive objects and massless particles moving in any static, conservative force field, not necessarily gravitational. In the case of the gravitational field of a static, spherically symmetric mass distribution, this metric turns out to be the Schwarzschild metric. This dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and also exactly reproduces the classical tests of General Relativity. In the second way, we obtain the RND metric directly, without first obtaining a Newtonian metric. Instead of conservation of energy, we use conservation of angular momentum, a carefully defined Newtonian limit and Tangherlini’s condition. The non-static case is handled by applying Lorentz covariance to the static case.

Relativistic quantum motion of the scalar bosons in the background space–time around a chiral cosmic string

In this paper, a relativistic behavior of spin-zero bosons is studied in a chiral cosmic string space–time. The Duffin–Kemmer–Petiau (DKP) equation and DKP oscillator are written in this curved space–time and are solved by using an appropriate ansatz and the Nikiforov–Uvarov method, respectively. The influences of the topology of this space–time on the DKP spinor and energy levels and current density are also discussed in detail.

Electron mobility in graphene without invoking the Dirac equation

The Dirac point and linear band structure in graphene bestow it with remarkable electronic and optical properties, a subject of intense ongoing research. Explanations of high electronic mobility in graphene often invoke the masslessness of electrons based on the effective relativistic Dirac-equation behavior, which are inaccessible to most undergraduate students and are not intuitive for non-physics researchers unfamiliar with relativity. Here, we show how to use only basic concepts from semiconductor theory and the linear band structure of graphene to explain its unusual effective mass and mobility, and compare them with conventional metals and semiconductors. We discuss the more intuitive concept of transverse effective mass, which emerges naturally from these basic derivations, and which approaches zero in the limit of undoped graphene at low temperature and is responsible for its extremely high mobility.

The missing piece: a new relativistic wave equation, the Pearcey equation

The relativistic wave equations currently used in physics are the Dirac equation and the Klein-Gordon equation. Only recently, the Salpeter equation has stimulated the interest of the scientific community. In this paper a new relativistic wave equation for particles with non-zero rest mass, the Pearcey equation, is presented. There is great formal similarity between the Pearcey equation, the Schrödinger equation and the Salpeter equation. In particular, the Pearcey equation allows us to understand the onset of the relativistic behaviour in a similar way as the Salpeter equation. It is possibile also to keep the parallelism between optics and quantum mechanics at which we are used in non relativistic quantum mechanics.

A geometric relativistic dynamics under any conservative force

Riemann’s principle “force equals geometry” provided the basis for Einstein’s General Relativity — the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The geometry of spacetime of a moving object is described by a metric obtained from the potential of the force field acting on it. We introduce a generalization of Newton’s First Law — the Generalized Principle of Inertia stating that: An inanimate object moves inertially, that is, with constant velocity, in its own spacetime whose geometry is determined by the forces affecting it. Classical Newtonian dynamics is treated within this framework, using a properly defined Newtonian metric with respect to an inertial lab frame. We reveal a physical deficiency of this metric (responsible for the inability of Newtonian dynamics to account for relativistic behavior), and remove it. The dynamics defined by the corrected Newtonian metric leads to a new Relativistic Newtonian Dynamics for both massive objects and massless particles moving in any static, conservative force field, not necessarily gravitational. This dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and also exactly reproduces the classical tests of General Relativity, as well as the post-Keplerian precession of binaries.

Raise and collapse of pseudo Landau levels in graphene

Lattice deformations couple to the low energy electronic excitations of graphene as vector fields similar to the electromagnetic potential \cite{SA02b,VKG10}. The suggestion that certain strain configurations would be able to induce pseudo landau levels in the spectrum of graphene \cite{GKG10,GGKN10}, and the subsequent experimental observation of these \cite{LBetal10} has been one of the most exciting events in an already fascinating field. It opened a new field of research "straintronics" linked to new applications, and had a strong influence on the physics of the new Dirac materials in two and three dimensions \cite{Amorim16}. The experimental observation of pseudo landau levels with scanning tunnel microscopy presents nevertheless some ambiguities. Similar strain patterns show different images sometimes difficult to interpret. In this work we strain the analogy of the pseudo versus real electromagnetic fields, as well as the fact that graphene has a relativistic behavior and show that, for some strain configurations, the deformation potential acts like a parallel electric field able to destabilize the Landau level structure via a mechanism identical to that described in \cite{LSB07,PC07} for real electromagnetic fields. The underlying physics is the combination of Maxwell electrodynamics and special relativity implying that different reference frames observe different electromagnetic fields \cite{LSB07}. The mechanism applies equally if the electric field has an external origin, which opens the door to an electric control of the giant pseudomagnetic fields in graphene.

Covariant response theory and the boost transform of the dielectric tensor

After a short critique of the Minkowski formulae for the electromagnetic constitutive laws in moving media, we argue that in actual fact the problem of Lorentz-covariant electromagnetic response theory is automatically solved within the framework of modern microscopic electrodynamics of materials. As an illustration, we first rederive the well-known relativistic transformation behavior of the microscopic conductivity tensor. Thereafter, we deduce from first principles the transformation law of the wavevector- and frequency-dependent dielectric tensor under Lorentz boost transformations.

A magnetic topological semimetal Sr1-yMn1-zSb2 (y, z < 0.1).

Weyl (WSMs) evolve from Dirac semimetals in the presence of broken time-reversal symmetry (TRS) or space-inversion symmetry. The WSM phases in TaAs-class materials and photonic crystals are due to the loss of space-inversion symmetry. For TRS-breaking WSMs, despite numerous theoretical and experimental efforts, few examples have been reported. In this Article, we report a new type of magnetic semimetal Sr1-yMn1-zSb2 (y, z < 0.1) with nearly massless relativistic fermion behaviour (m∗ = 0.04 - 0.05m0, where m0 is the free-electron mass). This material exhibits a ferromagnetic order for 304 K < T < 565 K, but a canted antiferromagnetic order with a ferromagnetic component for T < 304 K. The combination of relativistic fermion behaviour and ferromagnetism in Sr1-yMn1-zSb2 offers a rare opportunity to investigate the interplay between relativistic fermions and spontaneous TRS breaking.