In the paper, for the Kerr field, we prove that Chandrasekhar's Dirac Hamiltonian and the self‐adjoint Hamiltonian with a flat scalar product of the wave functions are physically equivalent. Operators of transformation of Chandrasekhar's Hamiltonian and wave functions to the η representation with a flat scalar product are defined explicitly. If the domain of the wave functions of Dirac's equation in the Kerr field is bounded by two‐dimensional surfaces of revolution around the z axis, Chandrasekhar's Hamiltonian and the self‐adjoint Hamiltonian in the η representation are Hermitian with equality of the scalar products, .
The interest to mesoscale dielectric objects, whose effective dimensions are comparable with the incident radiation wavelength, is caused by their unique ability to modify the spatial structure of the incident wave in the specific manner and to produce a highly localized intensive optical flux (“photonic jet”) with the subwavelength spatial resolution. In the current paper we brief review the modern state‐of‐the‐art of main principles of the photonic jet formation by non‐spherical and non‐symmetrical dielectric mesoscale particles both in transmitting and reflection mode. A deeper understanding of the photonic jet is nevertheless needed to fully exploit the potential performance of nano‐ and micro‐ dielectric mesoscale objects as diffractive components at different wavebands.
The quantum dynamics of a moving particle with a magnetic quadrupole moment that interacts with electric and magnetic fields is introduced. Then, it is discussed which conditions the external fields must satisfy so that an analogue of the Landau quantization can be obtained. Finally, by dealing with the lowest Landau level associated with the magnetic quadrupole system, an analogue of the quantum Hall conductivity is obtained.
Stefan W. Hell received the Nobel Prize in Chemistry in 2014 “for the development of super‐resolved fluorescence microscopy”, together with Eric Betzig and William Moerner. With the invention of STED (Stimulated Emission Depletion) microscopy experimentally realized in 1999, he has revolutionized light microscopy, overcoming the resolution limit of conventional optical microscopes – a breakthrough that has enabled new ground‐breaking discoveries in biological and medical research.
A new model of nonlinear electrodynamics with three parameters is suggested and investigated. It is shown that if the external constant magnetic field is present the phenomenon of vacuum birefringence takes place. The indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field are calculated. The electric field of a point‐like charge is not singular at the origin and the static electric energy is finite. We have calculated the static electric energy of point‐like particles for different parameters of the model. The canonical and symmetrical Belinfante energy‐momentum tensors and dilatation current are obtained. We demonstrate that the dilatation symmetry and dual symmetry are broken in the model suggested.
Van der Waals heterostructures of graphene and hexagonal boron nitride feature a moiré superlattice for graphene's Dirac electrons. Here, we review the effects generated by this superlattice, including a specific miniband structure featuring gaps and secondary Dirac points, and a fractal spectrum of magnetic minibands known as Hofstadter's butterfly.
In this paper, an implementation of energetic damping for fermionic transport simulations which respects particle conservation is presented. For this, nonhermitian terms in the Hamiltonian of the system are used. After an explanation of the method, it is demonstrated studying the current over time and I/V characteristics in the noninteracting resonant level model for spinless fermions.
It was previously argued that the phenomenon of quantum gravitational decoherence described by the Wheeler‐DeWitt equation is responsible for the emergence of the arrow of time. Here we show that the characteristic spatio‐temporal scales of quantum gravitational decoherence are typically logarithmically larger than a characteristic curvature radius of the background space‐time. This largeness is a direct consequence of the fact that gravity is a non‐renormalizable theory, and the corresponding effective field theory is nearly decoupled from matter degrees of freedom in the physical limit . Therefore, as such, quantum gravitational decoherence is too ineffective to guarantee the emergence of the arrow of time and the “quantum‐to‐classical” transition to happen at scales of physical interest. We argue that the emergence of the arrow of time is directly related to the nature and properties of physical observer.
Classes of solvable potentials are presented within an standard application of supersymmetric quantum mechanics. Sets of exceptional orthogonal polynomials generated by these solvable potentials are introduced and examined in detail. Several properties of these polynomials including orthogonality conditions, weight functions, differential equations, the Wronskains, possible recurrence relations are also investigated.
A new type of photonic crystal (PC) named graded index (GRIN) PC was proposed by E. Centeno in 2005. It is obtained by appropriately modifying the parameters of a regular PC, thus resulting in gradual index variation. Many applications are inspired by this notion. This review will introduce different ways of designing GRIN PCs from both theoretical and experimental point of views. Some typical applications based on GRIN PCs are presented, followed by the focusing mechanism of GRIN PC.
Nonlocal electrodynamics is a formalism developed to include nonlocal effects in the measurement process in order to account for the impossibility of instantaneous measurement of physical fields. This theory modifies Maxwell's electrodynamics by eliminating the hypothesis of locality that assumes an accelerated observer simultaneously equivalent to a comoving inertial frame of reference. In this scenario, the transformation between an inertial and accelerated observer is generalized which affects the properties of physical fields. In particular, we analyze how an uniformly accelerated observer perceives a homogeneous and isotropic black body radiation. We show that all nonlocal effects are transient and most relevant in the first period of acceleration.
We study the spin orientation of the neutron scattered by light‐irradiated graphene and calculate the average value of spin z‐component of the neutron in terms of a generating functional technique. Our calculation results indicate that there is a remarkable neutron polarization effect when a neutron penetrates graphene irradiated by a circularly polarized light. We analyse the dynamical source of generating this effect from the aspect of photon‐mediated interaction between the neutron spin and valley pseudospin. By comparing with the polarization induced by a magnetic field, we find that this polarization may be equivalent to the one led by a magnetic field of several hundred Teslas if the photon frequency is in the X‐ray frequency range. This provides an approach of polarizing neutrons.
Shuji Nakamura discovered p‐type doping in Gallium Nitride (GaN) and developed blue, green, and white “InGaN‐based” light emitting diodes (LEDs) and blue laser diodes (LDs). His inventions made possible energy efficient, solid‐state lighting systems and enabled the next generation of optical storage. In this biography, Shuji Nakamura tells the story of his personal life and his scientific career.
We present in total fifteen potentials for which the stationary Klein‐Gordon equation is solvable in terms of the confluent Heun functions. Because of the symmetry of the confluent Heun equation with respect to the transposition of its regular singularities, only nine of the potentials are independent. Four of these independent potentials are five‐parametric. One of them possesses a four‐parametric ordinary hypergeometric sub‐potential, another one possesses a four‐parametric confluent hypergeometric sub‐potential, and one potential possesses four‐parametric sub‐potentials of both hypergeometric types. The fourth five‐parametric potential has a three‐parametric confluent hypergeometric sub‐potential, which is, however, only conditionally integrable. The remaining five independent Heun potentials are four‐parametric and have solutions only in terms of irreducible confluent Heun functions.
Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two maximally symmetric spaces with two cosmological constants. We argue that the invariance of the bi‐field equations under projections on the separate spaces, may render one of the cosmological constants to zero. We also formulate the model in the presence of a scalar field. The resulted separate Einstein‐Eddington spaces maybe considered as two states that describe the universe before and after inflation. A possibly interesting affine action for a general perfect fluid is also proposed. It turns out that the condition which leads to zero cosmological constant in the vacuum case, eliminates here the effects of the gravitational mass density of the perfect fluid, and the dynamic of the universe in its final state is governed by only the inertial mass density of the fluid.
Single crystalline LiAlO is known as a very poor ion conductor. Thus, in its crystalline form it unequivocally disqualifies itself from being a powerful solid electrolyte in modern energy storage systems. On the other hand, its interesting crystal structure proves beneficial to sharpen our understanding of Li ion dynamics in solids which in return might influence application‐oriented research. LiAlO allows us to apply and test techniques that are sensitive to extremely slow Li ion dynamics. This helps us clarifying their diffusion behaviour from a fundamental point of view. Here, we combined two techniques to follow Li ion translational hopping in LiAlO that can be described by the same physical formalism: dynamic mechanical relaxation and electrical relaxation, i.e., ionic conductivity measurements. Via both methods we were able to track the same transport mechanism in LiAlO. Moreover, this enabled us to directly probe extremely slow Li exchange rates at temperatures slightly above 430 K. The results were compared with recent insights from nuclear magnetic resonance spectroscopy. Altogether, an Arrhenius‐type Li diffusion process with an activation energy of ca. 1.12 eV was revealed over a large dynamic range covering 10 orders of magnitude, i.e., spanning a dynamic range from the nano‐second time scale down to the second time scale.
A single particle obeys the Dirac equation in spatial dimensions and is bound by an attractive central monotone potential that vanishes at infinity. In one dimension, the potential is even, and monotone for The asymptotic behavior of the wave functions near the origin and at infinity are discussed. Nodal theorems are proven for the cases and , which specify the relationship between the numbers of nodes n1 and n2 in the upper and lower components of the Dirac spinor. For , whereas for if and if where and This work generalizes the classic results of Rose and Newton in 1951 for the case Specific examples are presented with graphs, including Dirac spinor orbits 相似文献
Optical properties of a metasurface which can be considered a monolayer of uniaxial metamaterials ‐ parallel‐plate and nanorod arrays – are investigated. It is shown that such metasurface acts as an ultimately thin sub‐100 nm wave plate. This is achieved via an interplay of epsilon‐near‐zero and epsilon‐near‐pole behavior along different axes in the plane of the metasurface allowing for extremely rapid phase difference accumulation in very thin metasurface layers. These effects are shown to not be disrupted by non‐locality and can be applied to the design of ultrathin wave plates, Pancharatnam‐Berry phase optical elements and plasmon‐carrying optical torque wrench devices.
Repulsive gravity is not very popular in physics. However, one comes across it in at least two main occurrences in general relativity: in the negative‐r region of Kerr spacetime, and as the result of the gravitational interaction between matter and antimatter, when the latter is assumed to be CPT‐transformed matter. Here we show how these two independent developments of general relativity are perfectly consistent in predicting gravitational repulsion and how the above Kerr negative‐r region can be interpreted as the habitat of antimatter. As a consequence, matter particles traveling along vortical geodesics can pass through the throat of a rotating black hole and emerge as antimatter particles (and vice versa). An experimental definitive answer on the gravitational behavior of antimatter is awaited in the next few years.
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