Algebraic classification of Weyl anomalies in arbitrary dimensions

Conformally invariant systems involving only dimensionless parameters are known to describe particle physics at very high energy. In the presence of an external gravitational field, the conformal symmetry may generalize to the Weyl invariance of classical massless field systems in interaction with gravity. In the quantum theory, the latter symmetry no longer survives: A Weyl anomaly appears. Anomalies are a cornerstone of quantum field theory, and, for the first time, a general, purely algebraic understanding of the universal structure of the Weyl anomalies is obtained, in arbitrary dimensions and independently of any regularization scheme.     

Electronic Bloch oscillation in a pristine monolayer graphene

In a pristine monolayer graphene subjected to a constant electric field along the layer, the Bloch oscillation of an electron is studied in a simple and efficient way. By using the electronic dispersion relation, the formula of a semi-classical velocity is derived analytically, and then many aspects of Bloch oscillation, such as its frequency, amplitude, as well as the direction of the oscillation, are investigated. It is interesting to find that the electric field affects the component of motion, which is non-collinear with electric field, and leads the particle to be accelerated or oscillated in another component.     

Weyl fermions on strings embedded in three dimensions

It is shown that the determinant of the Weyl operator introduced by Kavalov, Kostov and Sedrakyan is determined by the extrinsic geometry of the embedding. The effective action is anomalous under bendings of the surface.     

Electromagnetic Bloch oscillation in one-dimensional multiple microcavities composed of metamaterials

We propose a photonic structure stacked sequentially by one-dimensional photonic crystals and cavities. The whole structure is composed of single-negative and double-negative materials. The optical Wannier-Stark ladder （WSL） can be obtained in a low frequency region by modulating the widths of the cavities in order. We simulate the dynamical behavior of the electromagnetic wave passing through the proposed photonic structure. Due to the dispersive characteristics of the metamaterials, a very narrow WSL can be obtained. The long-period electromagnetic Bloch oscillation is demonstrated theoretically to have a period on a microsecond time scale.     

Bloch wave oscillation and Coulomb blockade in mesoscopic electric circuits

The quantum theory for mesoscopic electric circuits with charge discreteness is briefly described. The Schrödinger equation of the mesoscopic electric circuit with an external source which is the time function has been proposed. The Bloch wave oscillation and Coulomb blockade in the mesoscopic electric circuit have been addressed.     

Discriminating the Weyl type in higher dimensions using scalar curvature invariants

We consider higher dimensional Lorentzian spacetimes which are currently of interest in theoretical physics. It is possible to algebraically classify any tensor in a Lorentzian spacetime of arbitrary dimensions using alignment theory. In the case of the Weyl tensor, and using bivector theory, the associated Weyl curvature operator will have a restricted eigenvector structure for algebraic types II and D, which leads to necessary conditions on the discriminants of the associated characteristic equation which can be manifestly expressed in terms of polynomial scalar curvature invariants. The use of such necessary conditions in terms of scalar curvature invariants will be of great utility in the study and classification of black hole solutions in more than four dimensions.     

Classification of the Weyl curvature spinors of neutral metrics in four dimensions

Neutral geometry is of increasing interest. As with Riemannian and Lorentzian geometry, spinors can be expected to provide a valuable tool in neutral geometry. For a neutral metric in four dimensions, the classification of the Weyl curvature spinors by the pattern of principal spinors each admits is given. For each Weyl curvature spinor, there are nine nontrivial types. This classification is then related to the classification, given previously by the author, of a Weyl curvature spinor when regarded as a curvature endomorphism (four types). These results are the neutral analogues of well known and fundamental results in Lorentzian geometry, but display the peculiarities of neutral geometry. One can expect these results to be an essential ingredient in a full understanding of neutral geometry in four dimensions.     

Interplay between chiral magnetic and Kondo effects in Weyl metal phase

We investigate the Kondo effect in a Weyl metal state, which occurs from a spin-orbit coupled Dirac metal phase under magnetic fields. We start from an effective field theory in terms of low-energy fermions on a pair of chiral Fermi surfaces, which takes into account both the Berry curvature and chiral anomaly. Resorting to the U(1) slave-boson mean-field theory, we find that the effective Kondo temperature increases monotonically as a function of the external magnetic field due to enhancement of the density of states. The enhancement is originated from the chiral magnetic effect which is novel feature of Weyl metals. This leads to the prediction of the magnetic-field dependence in the logarithmic temperature dependence of the longitudinal magnetoconductivity.     

Optical Bloch oscillation and resonant Zener tunneling in one-dimensional quasi-period structures containing single negative materials

We studied the optical Bloch oscillation and resonant Zener tunneling in macroscopic quasi-period structures of alternatively stratified single negative and dielectric slabs. By a decrease in the thicknesses of the dielectric slabs, the electronic potential of crystals subjected to external dc electric fields is mimicked and the optical Wannier-Stark ladder (WSL) is realized. Both scattering states and the time-resolved transmission of a short pulse are provided to show the existence of the optical analogue of electronic Bloch oscillation. At a critical gradient, the resonant photon Zener tunneling is demonstrated both from the amplitude and the time delay in the transmitted signal of a short pulse.     

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions＇ Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.     

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions' Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.     

Selection rules for Bloch wave scattering for HREM imaging of imperfect crystals along symmetry axes

A Bloch wave analysis is used to investigate high-resolution electron microscope (HREM) imaging of crystals containing atomic displacements due to strain. In the absence of interband scattering, the shifts of peaks and troughs in the image will correspond to the displacements of the atoms in the exit surface. Interband scattering will shift the image peaks away from the actual atom positions and modify the apparent magnitude of the displacement identified by the observed image peak positions. By considering the case of seven-beam imaging of a cubic crystal aligned along a ?111? axis, it is shown that the symmetry of the Bloch waves leads to selection rules for the interband scattering, similar to those seen for dipole electron excitations in atoms. It is also shown that, to first order, no intraband scattering can occur.     

Bloch oscillation and Landau\ben Zener tunnelling in a modulated optical lattice in a photovoltaic photorefractive crystal

We theoretically study the beam dynamical behaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal.We find that two different Bloch oscillation patterns appear for the excitation of both broad and narrow light beams.One kind of optical Landau–Zener tunnelling also appears upon the Bloch oscillation and can be controlled by adjusting the parameter of the optical lattice.Unlike the case of linear potential,the energy radiation due to Landau–Zener tunnelling can be confined in modulated lattices of this kind.For high input intensity levels,the Landau–Zener tunnelling is suppressed by the photovoltaic photorefractive nonlinearity and a symmetry breaking of beam propagation from the modulational instability appears.     

Surface plasmon wave propagation along single metal wire

Recently,the single metal wire(SW) has become attractive for its potential applications in the terahertz and higher frequency range.However,as the most simple and typical surface plasmon polariton(SPP) transmission line,its study seems far from enough.Many important transmission behaviours have not been explained satisfactorily from the viewpoint of physics.In this paper,making use of the modified Drude model(MDM) based on the Sommerfeld theory,the transmission behaviours of SPPs along SW are systemically investigated theoretically.Some important physical phenomena such as the mode transformation,the lifetime of the radiative mode and the resonance frequency are revealed,and their mechanisms are explored.The results obtained in the paper will facilitate a general understanding of the features and the physical essence of the SPP transmission,not only for SW itself but also for other SPP transmission lines.     

Acoustic correlates of timbre space dimensions: a confirmatory study using synthetic tones

Timbre spaces represent the organization of perceptual distances, as measured with dissimilarity ratings, among tones equated for pitch, loudness, and perceived duration. A number of potential acoustic correlates of timbre-space dimensions have been proposed in the psychoacoustic literature, including attack time, spectral centroid, spectral flux, and spectrum fine structure. The experiments reported here were designed as direct tests of the perceptual relevance of these acoustical parameters for timbre dissimilarity judgments. Listeners presented with carefully controlled synthetic tones use attack time, spectral centroid, and spectrum fine structure in dissimilarity rating experiments. These parameters thus appear as major determinants of timbre. However, spectral flux appears as a less salient timbre parameter, its salience depending on the number of other dimensions varying concurrently in the stimulus set. Dissimilarity ratings were analyzed with two different multidimensional scaling models (CLASCAL and CONSCAL), the latter providing psychophysical functions constrained by the physical parameters. Their complementarity is discussed.     

Transitions in an atom moving along a metal surface

The probabilities of transitions in atoms moving along a metal surface are calculated.     

Characterization of the Weyl solutions

For the Weyl solutions(z, x) of the Schrödinger and Dirac equations, asymptotics for |z| are obtained. This gives a possibility of selecting Weyl solutions by their behaviour when |z| . Some applications are given.