In this article a particular solution of Heun equation is derived by making use of the Nikiforov‐Uvarov (NU) method which provides exact solutions for general hypergeometric equation and eigenvalues together with eigenfunctions of the Heun equation for this particular solution are obtained. One to one correspondence (isomorphism) of the aforesaid equation with the radial Schrödinger equation is emphasized and also physical counterparts of the parameters in this equation are put forward by introducing solutions for two different potential functions (Hulthen and Woods‐Saxon potentials).
A possible scenario of the Lorentz symmetry violation is discussed based on the arising of geometric quantum phases yielded by the effects of the Lorentz symmetry violation in the CPT‐even gauge sector of Standard Model Extension. Analogues of the Anandan quantum phase and the scalar Aharonov‐Bohm effect for a neutral particle [J. Anandan, Phys. Lett. A 138 , 347 (1989)] are obtained from the parity‐odd sector of the tensor . Moreover, we build quantum holonomies associated with the analogue of the Anandan quantum phase and discuss a possible analogy with the geometric quantum computation [A. Ekert et al., J. Mod. Opt. 47 , 2501 (2000)].
Ground‐state properties of the non‐interacting symmetric single‐impurity Anderson model (SIAM) are derived from the corresponding eigenenergy equation. Explicit formulae are given for the ground‐state energy, the hybridization, and the momentum distribution that are essential quantities for variational approaches to the interacting model. Various spectral functions, e.g., the total density of states, the phase shift function, and the impurity spectral function, are shown to agree with those obtained from the equation‐of‐motion method (see supplementary material). For a constant hybridization strength and a semi‐elliptic host density of states it is seen that the impurity spectral function builds up weight at the band edges.
The intrinsic lattice thermal conductivity of MoS2 is an important aspect in the design of MoS2‐based nanoelectronic devices. We investigate the lattice dynamics properties of MoS2 by first‐principle calculations. The intrinsic thermal conductivity of single‐layer MoS2 is calculated using the Boltzmann transport equation for phonons. The obtained thermal conductivity agrees well with the measurements. The contributions of acoustic and optical phonons to the lattice thermal conductivity are evaluated. The size dependence of thermal conductivity is investigated as well.
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.
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.
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.
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, .
A single spin‐1/2 particle obeys the Dirac equation in spatial dimension and is bound by an attractive central monotone potential which vanishes at infinity (in one dimension the potential is even). This work refines the relativistic comparison theorems which were derived by Hall 1 . The new theorems allow the graphs of the two comparison potentials and to crossover in a controlled way and still imply the spectral ordering for the eigenvalues at the bottom of each angular momentum subspace. More specifically in a simplest case we have: in dimension , if , then ; and in dimensions, if , where and , then .
In fiber lasers, the study of the cubic‐quintic complex Ginzburg‐Landau equations (CGLE) has attracted much attention. In this paper, four families (kink solitons, gray solitons, Y‐type solitons and combined solitons) of exact soliton solutions for the variable‐coefficient cubic‐quintic CGLE are obtained via the modified Hirota method. Appropriate parameters are chosen to investigate the properties of solitons. The influences of nonlinearity and spectral filtering effect are discussed in these obtained exact soliton solutions, respectively. Methods to amplify the amplitude and compress the width of solitons are put forward. Numerical simulation with split‐step Fourier method and fourth‐order Runge‐Kutta algorithm are carried out to validate some of the analytic results. Transformation from the variable‐coefficient cubic‐quintic CGLE to the constant coefficients one is proposed. The results obtained may have certain applications in soliton control in fiber lasers, and may have guiding value in experiments in the future.
This is a personal history of one of the Japanese researchers engaged in developing a method for growing GaN on a sapphire substrate, paving the way for the realization of smart television and display systems using blue LEDs. The most important work was done in the mid to late 1980s. The background to the author's work and the process by which the technology enabling the growth of GaN and the realization of p‐type GaN was established are reviewed. ***
A fiber laser based on random distributed feedback has attracted increasing attention in recent years, as it has become an important photonic device and has found wide applications in fiber communications or sensing. In this article, recent advances in high‐power random distributed feedback fiber laser are reviewed, including the theoretical analyses, experimental approaches, discussion on the practical applications and outlook. It is found that a random distributed feedback fiber laser can not only act as an information photonics device, but also has the feasibility for high‐efficiency/high‐power generation, which makes it competitive with conventional high‐power laser sources. In addition, high‐power random distributed feedback fiber laser has been successfully applied for midinfrared lasing, frequency doubling to the visible and high‐quality imaging. It is believed that the high‐power random distributed feedback fiber laser could become a promising light source with simple and economic configurations.
Single neutral atom mechanics is controllable by focused, high‐intensity optical vortices. The intensity‐dependent, laser‐driven motion of the atom's active electrons subsumes to a net transfer of the orbital angular momentum of the light to the neutral atom. The ponderomotive force on these electrons translates so into an unbounded or a bounded radial drift of the atom depending on its initial kinetic energy, as set by the temperature. Appropriate combination of laser beams results in sub‐wavelength, dynamical radial traps for tweezing atoms controllably, an effect that can be exploited for atom guiding, structuring, and lithographic applications.
Uniform, graded and spaced arrays of 3 μm triangular antidots in pulsed laser deposited YBa2Cu3O7 (YBCO) superconducting thin films are compared by examining the improvements in the critical current density they produced. The comparison is made to establish the role of their lithographically defined (non‐)uniformity and the effectiveness to control and/or enhance the critical current density. It is found that almost all types of non‐uniform arrays, including graded ones enhance over the broad applied magnetic field and temperature range due to the modified critical state. Whereas uniform arrays of antidots either reduce or produce no effect on compared to the original (as‐deposited) thin films.
Isamu Akasaki is known for inventing the bright gallium nitride (GaN) p‐n junction blue LED in 1989 and subsequently the high‐brightness GaN blue LED. Together with Shuji Nakamura and Hiroshi Amano, he is one of the three recipients of the 2014 Nobel Prize in Physics. In his Nobel Lecture, he describes the historical progress that led to the invention of the first p‐n junction blue/UV LED and related optical devices. ***
The doubly special relativity (DSR) theories are suggested in order to incorporate an observer‐independent length scale in special theory of relativity. The Magueijo‐Smolin proposal of DSR is realizable through a particular form of the noncommutative (NC) spacetime (known as κ‐Minkowski spacetime) in which the Lorentz symmetry is preserved. In this framework, the NC parameter κ provides the origin of natural cutoff energy scale. Using a nonlinear deformed relativistic dispersion relation along with the Lorentz transformations, we investigate some phenomenological facets of two‐body collision problem (without creation of new particles) in a κ‐Minkowski spacetime. By treating an elastic scattering problem, we study effects of the Planck scale energy cutoff on some relativistic kinematical properties of this scattering problem. The results are challenging in the sense that as soon as one turns on the κ‐spacetime extension, the nature of the two‐body collision alters from elastic to inelastic one. It is shown also that a significant kinematical variable involving in heavy ion collisions, the rapidity, is not essentially an additive quantity under a sequence of the nonlinear representation of the Lorentz transformations.
In this paper, we address the implications when a homogeneous dust model is considered for a scenario of gravitational collapse in the context of Eddington‐inspired Born‐Infeld (EiBI) theory. In order to describe the dynamical evolution of the collapse, we present an effective equation, which constitutes the first order corrections, in EiBI coupling parameter κ, to Einstein's field equations. The geometry outside the collapsing object is derived by imposing the standard Darmois‐Israel junction conditions at the boundary surface of the dust. This induces an effective matter source in the outer region which gives rise to a non‐singular, non‐Schwarzschild geometry at the final state of the collapse. For this exterior geometry, we find the threshold of mass for the formation of the black hole. This provides a cut‐off over κ as .
A theoretical analysis of the resonance fluorescence of a two‐level atom in a classical monochromatic field with feedback phase switching depending on the fluorescence triplet component which the last spontaneously emitted photon belongs to is presented. The considered feedback loop is a hybrid quantum‐classical system. Statistics of photoemissions into the triplet components is investigated as well as correlations between the components. In contrast to the well‐known resonance fluorescence of a two‐level atom without feedback phase switching, a bunching of photocounts is predicted in each side‐band, and successive photoemissions into different side‐bands manifest antibunching. The type of the statistics can efficiently be controlled by the frequency detuning of the external field. In many points the considered feedback scheme provides drastically different statistical features of fluorescence when compared with the scheme of frequency‐unselective feedback phase switching.
We present a feasible protocol of continuous variable quadripartite entanglement from the coupled type I second harmonic generation (SHG) below threshold. According to the sufficient inseparability criteria for multipartite continuous variable (CV) entanglement, the four output fields are proved to be multicolored entangled beams in separable locations with four‐mode amplitude quadratures correlation and relative phase quadratures correlation. It shows that the coupled system can produce a compact tunable multimode entangled source that can be applied into the quantum communication.
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