Defects and frequently used defect models of solids are reviewed. Signatures for identifying the disorder from x‐ray and neutron scattering data are given. To give illustrative examples how technologically important defects contribute to x‐ray and neutron scattering numerical method able to treat non‐periodical solids possessing several simultaneous defect types is given for simulating scattering in nanosize disordered clusters. The approach takes particle size, shape, and defects into account and isolates element specific signals. As a case study a statistical approximation model for lead‐zirconate titanate [Pb(ZrxTi)O3, PZT] is introduced. PZT is a material possessing several defect types, including substitutional, displacement and surface defects. Spatial composition variation is taken into account by introducing a model in which the edge lengths of each cell depend on the distribution of Zr and Ti ions in the cluster. Spatially varying edge lengths and angles is referred to as microstrain. The model is applied to compute the scattering from ellipsoid shaped PZT clusters and to simulate the structural changes as a function of average composition. Two‐phase co‐existence range, the so called morphotropic phase boundary composition is given correctly. The composition at which the rhombohedral and tetragonal cells are equally abundant was . Selected x‐ray and neutron Bragg reflection intensities and line shapes were simulated. Examples of the effect of size and shape of the scattering clusters on diffraction patterns are given and the particle dimensions, computed through Scherrer equation, are compared with the exact cluster dimensions. Scattering from two types of 180° domains in spherical particles, one type assigned to Ti‐rich PZT and the second to the MPB and Zr‐rich PZT, is computed. We show how the method can be used for modelling polarization reversal.
In modern Kaluza‐Klein theories which successfully unify gravity, electromagnetism and a scalar field, null geodesics in five dimensions lead to simplified expressions for phase shifts in four‐dimensional spacetime. It might be possible to test for an extra dimension by experiments such as those where neutron interferometry is used to measure the Aharonov‐Bohm effect.
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.
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 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 .
Analytical solutions of the Schrödinger equation for the one‐dimensional quantum well with all possible permutations of the Dirichlet and Neumann boundary conditions (BCs) in perpendicular to the interfaces uniform electric field are used for the comparative investigation of their interaction and its influence on the properties of the system. Limiting cases of the weak and strong voltages allow an easy mathematical treatment and its clear physical explanation; in particular, for the small , the perturbation theory derives for all geometries a linear dependence of the polarization on the field with the BC‐dependent proportionality coefficient being positive (negative) for the ground (excited) states. Simple two‐level approximation elementary explains the negative polarizations as a result of the field‐induced destructive interference of the unperturbed modes and shows that in this case the admixture of only the neighboring states plays a dominant role. Different magnitudes of the polarization for different BCs in this regime are explained physically and confirmed numerically. Hellmann‐Feynman theorem reveals a fundamental relation between the polarization and the speed of the energy change with the field. It is proved that zero‐voltage position entropies are BC independent and for all states but the ground Neumann level (which has ) are equal to while the momentum entropies depend on the edge requirements and the level. Varying electric field changes position and momentum entropies in the opposite directions such that the entropic uncertainty relation is satisfied. Other physical quantities such as the BC‐dependent zero‐energy and zero‐polarization fields are also studied both numerically and analytically. Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.
We determine the regularized van der Waals contribution to pressure within a spherical cavity of vapor in a homogeneous, isotropic, infinite medium. The spherical Hamaker function, , has been defined, for the first time, in contrast to the conventional Hamaker function for planar surfaces, . For the materials under consideration, the pressure inside the cavity varies as , where a is the radius of the cavity. For radii below a transition radius, the surface energy (or surface tension) becomes size dependent and could have important implications for homogeneous nucleation of nanosized bubbles in liquids, as well as cavitation of bubbles.
The circular dichroism of titanium‐doped silver chiral nanorod arrays grown using the glancing angle deposition (GLAD) method is investigated in the visible and near infrared ranges using transmission ellipsometry and spectroscopy. These films are found to have significant circular polarization effects across broad ranges of the visible to NIR spectrum, including large values for optical rotation. The characteristics of these circular polarization effects are strongly influenced by the morphology of the deposited arrays. Thus, the morphological control of the optical activity in these nanostructures demonstrates significant optimization capability of the GLAD technique for fabricating chiral plasmonic materials.
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, .
α,ω‐Dithiols present an interesting case of molecules with two reactive terminal ‐SH groups (HS‐R‐SH) that allow their use as binders between different metallic entities. They have thus been used in molecular electronics conduction measurements, in “nanogap” electrodes of interest in plasmonics, as building blocks of more complex structures such as metal intercalated superlattices and in the formation of metalized organic thin films, including doped graphene type films. There exist however many problems, because the molecules may end up in undesirable configurations with both thiol terminals bound to the same metal particle/substrate or link with other molecules to produce “multi‐molecule” or “multilayer” structures. This report discusses various key questions on dithiol linking with metal surfaces and the quest of protocols of making problem free dithiol metal structures. It then describes the use of dithiols and their SAMs to produce various metal organic heterostructures useful for molecular electronics and formation of doped metalized organic thin films. We discuss the build up of these structures by self assembly and lithography, their chemical composition and functional properties.
The so‐called Jackiw–Pi (JP) model for massive vector fields is a three‐dimensional, gauge‐invariant and parity‐preserving model that was discussed in several contexts. In this paper we have discussed its quantum aspects through the introduction of Planck‐scale objects, i.e., via noncommutativity and the well‐known BV quantization. Namely, we have constructed the JP noncommutative space‐time version, we have provided the BV quantization of the commutative JP model and we have discussed its features. The noncommutativity has introduced interesting new objects in JP's Planck‐scale framework.
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.
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.
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.
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.
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.
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)].
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.
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.
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. Together with Isamu Akasaki and Hiroshi Amano, he is one of the three recipients of the 2014 Nobel Prize in Physics. In his Nobel lecture, Shuji Nakamura gives an overview of this research and the story of his inventions *** .
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