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 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, .
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.
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.
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.
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.
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.
We present a general methodology for electromagnetic homogenization and characterization of bianisotropic metasurfaces formed by regular or random arrangements of small arbitrary inclusions at interfaces of two different isotropic media. The approach unites and generalizes the earlier theories developed independently by two joint research groups: that of profs. Holloway and Kuester and that of profs. Simovski and Tretyakov. We analyze the features of both formalisms and discuss their peculiarities in several example cases. Our theory can be used in the analysis and synthesis of a wide spectrum of metasurfaces.
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 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)].
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 .
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.
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.
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 *** .
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. ***
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 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).
Uncertainties in successive measurements of general canonically conjugate variables are examined. Such operators are approached within a limiting procedure of the Pegg–Barnett type. Dealing with unbounded observables, we should take into account a finiteness of detector resolution. An appropriate reformulation of two scenarios of successive measurements is proposed and motivated. Uncertainties are characterized by means of generalized entropies of both the Rényi and Tsallis types. The Rényi and Tsallis formulations of uncertainty relations are obtained for both the scenarios of successive measurements of canonically conjugate operators. Entropic uncertainty relations for the cases of position and momentum are separately discussed.
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