Quadratic Weyl points in metacrystals

The discovery of new topological states has become an important goal in the multidisciplinary fields of physics and material science [1,2]. In addition to topological insulators,topological semimetals without band gaps have been the focus of research efforts. Typical examples include Weyl and Dirac semimetals, which feature isolated 2-band and 4-band linear crossing points in their band structures.     

Lifshitz transitions via the type-II dirac and type-II Weyl points

The type-II Weyl and type-II Dirac points emerge in semimetals and in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. In one case, the type-II Weyl point connects the Fermi pockets, and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case, the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition, the Weyl point is released from both Fermi surfaces. They loose their Berry flux, which guarantees the global stability, and without the topological support, the inner surface disappears after shrinking to a point at the second Lifshitz transition. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds.     

Fixed points in interacting dark energy models

The dynamical behaviors of two interacting dark energy models are considered. In addition to the scaling attractors found in the non-interacting quintessence model with exponential potential, new accelerated scaling attractors are also found in the interacting dark energy models. The coincidence problem is reduced to the choice of parameters in the interacting dark energy models.     

Type-I Weyl points induced by negative coupling in photonic crystal

Weyl points, which are the degenerate points in three-dimensional momentum space, have been widely studied in the photonic system, and show some intriguing phenomena such as topologically protected surface states and chiral anomalies. Type-I Weyl systems possess a complete bandgap, and topologically protected surface states can be excited without disturbing the bulk states.In this work, we investigate the influence of the sign of coupling coefficient on the topological property of the system and find that type-I Weyl points can be realized by introducing a negative coupling between the stacking layers of the designed photonic crystal. We propose a new strategy to construct a type-I Weyl system by stacking the hexagonal photonic lattice. Different from the topological nontrivial photonic system with a positive coefficient, the negative couplings in the photonic system are realized by adding another resonating site between stacking layers. We theoretically demonstrate that the effective coupling between the resonating sites in adjacent layers sign-flips through the judicious design of the nearest coupling strength and eigenfrequency of the additional sites. The surface states at opposite boundaries of the proposed system have opposite group velocities, which is the feature of type-I Weyl points. Our study provides a new method of exploring topologically protected photonic systems and developing possible topological devices.     

Bianchi Type-III String Cosmological Models

Bianchi type III space time is considered in the presence of cosmic strings in Einstein’s general theory of relativity. Exact cosmological models are presented with the help of relation C=B ⁿ between metric coefficients C and B. Some physical properties of the model in each cases are discussed.     

Weyl geometry

We develop the properties of Weyl geometry, beginning with a review of the conformal properties of Riemannian spacetimes. Decomposition of the Riemann curvature into trace and traceless parts allows an easy proof that the Weyl curvature tensor is the conformally invariant part of the Riemann curvature, and shows the explicit change in the Ricci and Schouten tensors required to insure conformal invariance. We include a proof of the well-known condition for the existence of a conformal transformation to a Ricci-flat spacetime. We generalize this to a derivation of the condition for the existence of a conformal transformation to a spacetime satisfying the Einstein equation with matter sources. Then, enlarging the symmetry from Poincaré to Weyl, we develop the Cartan structure equations of Weyl geometry, the form of the curvature tensor and its relationship to the Riemann curvature of the corresponding Riemannian geometry. We present a simple theory of Weyl-covariant gravity based on a curvature-linear action, and show that it is conformally equivalent to general relativity. This theory is invariant under local dilatations, but not the full conformal group.     

Weyl gravitoelectromagnetism

We study the gauge transformation in the context of gravitoelectromagnetism and introduce a new expression for the phase factor. Using these concepts and with the principle of local gauge invariance applied to physical theories, a formal derivation of gravitoelectromagnetism is obtained.     

Plane Symmetric Vacuum Bianchi Type-III Cosmological Model in Brans-Dicke Theory

We have obtained an exact solution of the vacuum Brans-Dicke (Phys. Rev. 124:925, 1961) field equations for the metric tensor of a spatially homogeneous and anisotropic model. Some physical properties of the model are also studied.     

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.     

拓扑Weyl半金属简介

材料体系的拓扑量子行为是当前凝聚态物理研究的热点。作为一种新型拓扑量子态,Weyl半金属最近引起了人们的关注。文章以烧绿石结构铱氧化物A₂Ir₂O₇(其中A=Y或稀土元素)为例,介绍了Weyl半金属的奇特性质：Weyl点受拓扑保护稳定;Weyl半金属有着受拓扑保护的表面态,即非闭合的费米弧;Weyl半金属的反常霍尔效应与Weyl点的位置有关,和能带的细节无关;Weyl半金属特有的输运性质。文章还介绍了人们预言的几种Weyl半金属以及相关的实验进展。     

Localization and the Weyl algebras

Physics of Atomic Nuclei - Let W n (ℝ) be the Weyl algebra of index n. It is well known that so(p, q) Lie algebras can be viewed as quadratic polynomial (Lie) algebras in W n (ℝ) for p...     

Weyl quantization and star products

Many non-linear classical mechanical systems arise as the symplectic reductions of linear systems. The star products on the corresponding quantized algebras can be derived from the Weyl-Moyal product on the algebras of the linear systems. An algebraic approach to Berezin quantization is sketched.     

Euclidean Majorana and Weyl Spinors

The complex form algebra of Schwinger functions of a Dirac field on a Euclidean R ^d with arbitrary dimension d is decomposed into the form algebras of Majorana spinors and of Weyl spinors. The existence of real form algebras is investigated. The reality condition leads to severe restrictions in the case of Majorana forms which do not agree with the results of classical field theory. For all real form algebras Euclidean spinors are constructed as elements of a measure space.     

Two interacting particles in a disordered chain IV: Scaling of level curvatures

The curvatures of two-particle energy levels with respect to the enclosed magnetic flux in mesoscopic disordered rings are investigated numerically. We find that the typical value of the curvatures is increased by interactions in the localised regime and decreased in the metallic regime. This confirms a prediction by Akkermans and Pichard (Eur. Phys. J. B 1, 223 (1998)). The interaction-induced changes of the typical curvatures at different energies and disorder strengths exhibit one-parameter scaling with a conductance-like single parameter. This suggests that interactions could influence the conductance of mesoscopic systems similarly. Received 24 August 1998     

Weyl quantization and metaplectic representation

The formal expansion defining the twisted exponential of an element of the Lie algebra _n ( ⁿ Sp(2, )) can be summed and this result is used to explicitly obtain the classical function u _t corresponding to an evolution operator associated to a quantum Hamiltonian belonging to the above mentioned Lie algebra.Then, by applying the Weyl quantization procedure to u _t we get a representation of the group W _n ( ⁿ Sp(2, )) in terms of integral operators, the kernels of which are expressed by means of the classical action. The family u _t being only locally defined, it must be considered as a distribution on the classical phase space in order to get the metaplectic representation.Membres du Centre National de la Recherche Scientifique.     

Bianchi Type-III Dark Energy Model in a Saez-Ballester Scalar-Tensor Theory

In this paper, we investigate Bianchi type-III universe which has dynamical energy density. We introduce three different skewness parameters along spatial directions to quantify the deviation of pressure from isotropy. We also assume that the skewness parameters are time dependent. The Saez-Ballester (J. Phys. Lett. A 113:467, 1986) field equations have been solved by applying a variation law for generalized Hubble’s parameter given by Bermann (Nuovo Cimento B 74:182, 1983). Some physical and kinematical properties of dark energy model are discussed.