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).
We consider a universe with a bulk viscous cosmic fluid, in a flat Friedmann‐Lemaitre‐Robertson‐Walker geometry. We derive the conditions for the existence of inflation, and those which at the same time prevent the occurrence of self‐reproduction. Our theoretical model gives results which are in perfect agreement with the most recent data from the PLANCK surveyor.
The FeTe parent compound for iron‐superconductor chalcogenides was studied applying Mössbauer spectroscopy accompanied by ab initio calculations of electric field gradients at the iron nuclei. Room‐temperature (RT) Mössbauer spectra of single crystals have shown asymmetric doublet structure commonly ascribed to contributions of over‐stoichiometric iron or impurity phases. Low‐temperature Mössbauer spectra of the magnetically ordered compound could be well described by four hyperfine‐split sextets, although no other foreign phases different from Fe1.05Te were detected by XRD and microanalysis within the sensitivity limits of the equipment. Density functional ab initio calculations have shown that over‐stoichiometric iron atoms significantly affect electron charge and spin density up to the second coordination sphere of the iron sub‐lattice, and, as a result, four non‐equivalent groups of iron atoms are formed by their local environment. The resulting four‐group model consistently describes the angular dependence of the single crystals Mössbauer spectra as well as intensity asymmetry of the doublet absorption lines in powdered samples at RT. We suppose that our approach could be extended to the entire class of FeSeTex compounds, which contain excess iron atoms.
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 .
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.
Recently, compressed H2S has been shown to become superconducting at 203 K under a pressure of 155 GPa. One might expect fluctuations to dominate at such temperatures. Using the magnetisation critical current, we determine the ground‐state London penetration depth, λ0=189 nm, and the superconducting energy gap, Δ0=27.8 meV, and find these parameters are similar to those of cuprate superconductors. We also determine the fluctuation temperature scale, K, which shows that, unlike the cuprates, of the hydride is not limited by fluctuations. This is due to its three dimensionality and suggests the search for better superconductors should refocus on three‐dimensional systems where the inevitable thermal fluctuations are less likely to reduce the observed .
A fundamental problem regarding the Dirac quantization of a free particle on an () curved hypersurface embedded in N flat space is the impossibility to give the same form of the curvature‐induced quantum potential, the geometric potential as commonly called, as that given by the Schrödinger equation method where the particle moves in a region confined by a thin‐layer sandwiching the surface. This problem is resolved by means of a previously proposed scheme that hypothesizes a simultaneous quantization of positions, momenta, and Hamiltonian, among which the operator‐ordering‐free section is identified and is then found sufficient to lead to the expected form of geometric potential. 相似文献
The Bañados‐Teitelboim‐Zanelli (BTZ) black hole model corresponds to a solution of (2+1)‐dimensional Einstein gravity with negative cosmological constant, and by a conformal rescaling its metric can be mapped onto the hyperbolic pseudosphere surface (Beltrami trumpet) with negative curvature. Beltrami trumpet shaped graphene sheets have been predicted to emit Hawking radiation that is experimentally detectable by a scanning tunnelling microscope. Here, for the first time we present an analytical algorithm that allows variational solutions to the Dirac Hamiltonian of graphene pseudoparticles in BTZ black hole gravitational field by using an approach based on the formalism of pseudo‐Hermitian Hamiltonians within a discrete‐basis‐set method. We show that our model not only reproduces the exact results for the real part of quasinormal mode frequencies of (2+1)‐dimensional spinless BTZ black hole, but also provides analytical results for the real part of quasinormal modes of spinning BTZ black hole, and also offers some predictions for the observable effects with a view to gravity‐like phenomena in a curved graphene sheet.
By considering (non‐relativistic) quantum mechanics as it is done in practice in particular in condensed‐matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope, leaving a lot of room for embedding the quantum‐classical transition into our current theories without recurring to difficult‐to‐accept interpretations of quantum mechanics. Nonunitary projections to initial and final states, the breaking of time‐reversal symmetry, a change of Hilbert space, and the introduction of classical concepts such as external potentials or localized atomic nuclei are widespread in quantum mechanical calculations. Furthermore, quantum systems require classical environments that enable the symmetry breaking that is necessary for creating the atomic configurations of molecules and crystals. This paper argues that such classical environments are provided by finite‐temperature macroscopic systems in which the range of quantum correlations and entanglement is limited. This leads to classical behavior on larger scales, and to collapse‐like events in all dynamical processes that become coupled to the thermalized degrees of freedom.
A mechanism of amplification of surface plasmon polaritons due to the transfer of electromagnetic energy from a drift current wave into a far‐infrared surface wave propagating along a semiconductor‐dielectric boundary in waveguide geometry is proposed. A necessary condition of the interaction of these waves is phase matching condition, i. e., when the phase velocity of the surface wave approaches the drift velocity of charge carriers. It is shown that in the spectral region of the surface plasmon polariton slowing‐down its amplification coefficient can reach values substantially exceeding the ohmic loss coefficient of the surface wave in the structure.
The properties of the superconducting and the anomalous normal state were described by using the Eliashberg method. The pairing mechanism was reproduced with the help of the Hamiltonian, which models the electron‐phonon and the electron‐electron‐phonon interaction (EEPh). The set of the Eliashberg equations, which determines the order parameter function (φ), the wave function renormalization factor (Z), and the energy shift function (χ), was derived. It was proven that for the sufficiently large values of the EEPh potential, the doping dependence of the order parameter () has the analogous course to that observed experimentally in cuprates. The energy gap in the electron density of states is induced by Z and χ ‐ the contribution from φ is negligible. The electron density of states possesses the characteristic asymmetric form and the pseudogap is observed above the critical temperature.
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 theory of dielectric response of water under nanoscale confinement was long overdue. This work addresses the problem by establishing a relation between dielectric response and hydrogen‐bond frustration subsumed in a non‐Debye polarization term. The results hold down to the single‐molecule contribution and are validated vis‐à‐vis experimental measurements on a system where dielectric modulation entails removal of a single water molecule. The frustrated dielectric response down to molecular scales is assessed by contrasting two enantiomeric ligands in association with the same protein, with the complexes differing in the removal of a single interfacial water molecule.
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.
We analyze how a multilevel many‐electron system in a photon cavity approaches the steady state when coupled to external leads. When a plunger gate is used to lower cavity photon dressed one‐ and two‐electron states below the bias window defined by the external leads, we can identify one regime with nonradiative transitions dominating the electron transport, and another regime with radiative transitions. Both transitions trap the electrons in the states below the bias bringing the system into a steady state. The order of the two regimes and their relative strength depends on the location of the bias window in the energy spectrum of the system and the initial conditions.
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 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.
A comparative analysis of three different time‐independent approaches to studying open quantum structures in a uniform electric field was performed using the example of a one‐dimensional attractive or repulsive δ‐potential and the surface that supports the Robin boundary condition. The three considered methods exploit different properties of the scattering matrix as a function of energy E: its poles, real values, and zeros of the second derivative of its phase. The essential feature of the method of zeroing the resolvent, which produces complex energies, is the unlimited growth of the wave function at infinity, which is, however, eliminated by the time‐dependent interpretation. The real energies at which the unitary scattering matrix becomes real correspond to the largest possible distortion, , or its absence at which in either case leads to the formation of quasibound states. Depending on their response to the increasing electric intensity, two types of field‐induced positive energy quasibound levels are identified: electron‐ and hole‐like states. Their evolution and interaction in the enlarging field lead ultimately to the coalescence of pairs of opposite states, with concomitant divergence of the associated dipole moments in what is construed as an electric breakdown of the structure. The characteristic features of the coalescence fields and energies are calculated and the behavior of the levels in their vicinity is analyzed. Similarities between the different approaches and their peculiarities are highlighted; in particular, for the zero‐field bound state in the limit of the vanishing , all three methods produce the same results, with their outcomes deviating from each other according to growing electric intensity. The significance of the zero‐field spatial symmetry for the formation, number, and evolution of the electron‐ and hole‐like states, and the interaction between them, is underlined by comparing outcomes for the symmetric δ geometry and asymmetric Robin wall.
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.
Asymmetric metal‐dielectric nanostructures are demonstrated superior optical properties arising from the combination of strong enhancement of near‐fields and controllable scattering characteristics which originate from plasmonic and high‐index dielectric components. Here, being inspired by the recent advances of the asymmetric hybrid nanoparticles fabrication [Dmitry Zuev, et al., Adv. Mater. 28 , 3087 (2016)], we suggest and study numerically a novel type of hybrid dimer nanoantennas. The nanoantennas consist of asymmetric metal‐dielectric (Au/Si) nanoparticles and allow tuning of the near‐ and far‐field properties via laser induced reshaping of the metal part at the nanoscale. We demonstrate an ability to modification of the scattering properties, near‐field distribution profilis, normalized local density of states, and radiation patterns of the nanoantenna upon the laser reshaping. The parameters used to investigate these effects correspond to experimentally demonstrated values.
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