硅烯中受电场调控的体能隙和朗道能级

近年来, 硅烯(单层硅)由于其独特的结构和电子性质以及在量子霍尔效应等领域的潜在应用而成为理论和实验研究的一个热点. 借助于四带次近邻紧束缚模型, 详细计算和研究了硅烯中受电场调制的体能隙和电子能级. 结果表明: 硅烯原胞中的两个子格处于不同的平面上, 可以通过外电场区分和控制这两个子格, 这将破坏在纯石墨烯中无法被破坏的K-K'对称性, 并消除由这一对称性导致的电子能级的二重简并; 外加电场还会引起硅烯中次近邻格点之间的Rashba自旋轨道耦合, 这一作用会在不同狄拉克点有选择地消除电子能级在部分电场点的简并, 相邻能级从交叉状态变为反交叉状态; 电子能级中除一些孤立的交叉点外, 每个能级都具有确定的自旋取向, 石墨烯中电子能级的四重简并在硅烯中被完全消除, 从而导致填充因子ν=0, ±1, ±2, ±3,…的量子霍尔平台.     

Ginzburg–Landau functionals and renormalized energy: A revised Γ-convergence approach

We give short and self-contained proofs of Γ-convergence results for Ginzburg–Landau energy functionals in two dimensions, in the logarithmic energetic regime. In particular, we derive the renormalized energy by Γ-convergence.     

Global Continuity of the Integrated Density of States for Random Landau Hamiltonians

Abstract

We prove that the integrated density of states (IDS) for the randomly perturbed Landau Hamiltonian is Hölder continuous at all energies with any Hölder exponent 0 < q < 1. The random Anderson-type potential is constructed with a nonnegative, compactly supported single-site potential u. The distribution of the iid random variables is required to be absolutely continuous with a bounded, compactly supported density. This extends a previous result Combes et al. [Combes, J. M., Hislop, P. D., Klopp, F. (2003a). Hölder continuity of the integrated density of states for some random operators at all energies. Int. Math. Res. Notices 2003: 179--209] that was restricted to constant magnetic fields having rational flux through the unit square. We also prove that the IDS is Hölder continuous as a function of the nonzero magnetic field strength.     

Casimir effect for a scalar field via Krein quantization

In this work, we present a rather simple method to study the Casimir effect on a spherical shell for a massless scalar field with Dirichlet boundary condition by applying the indefinite metric field (Krein) quantization technique. In this technique, the field operators are constructed from both negative and positive norm states. Having understood that negative norm states are un-physical, they are only used as a mathematical tool for renormalizing the theory and then one can get rid of them by imposing some proper physical conditions.     

Non-compact Groups,Coherent States,Relativistic Wave Equations and the Harmonic Oscillator

Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in the correct interpretation of the square root Hamiltonian, is used. The obtained spectrum of physical states and the Fock construction consist of Squeezed States which correspond to the representations with the lowest weights and with four possible (non-trivial) fractional representations for the group decomposition of the spin structure. From the theory of semigroups the analytical representation of the radical operator in the superspace is constructed, the conserved currents are computed and a new relativistic wave equation is proposed and explicitly solved for the time-dependent case. The relation with the Relativistic Schr?dinger equation and the Time-dependent Harmonic Oscillator is analyzed and discussed.      

An algebraic index theorem for orbifolds

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann-Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the Kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem.     

Wavelets in Banach Spaces

We describe a construction of wavelets (coherent states) in Banach spaces generated by admissible group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an example, we consider operator-valued Segal–Bargmann-type spaces and the Weyl functional calculus.     

A nonconvex dissipative system and its applications (II)

This paper presents exact solutions in terms of implicit functions and hyperbolic functions to a nonconvex dissipative system, controlled by a Duffing–van der Pol nonlinear equation with a fifth-order nonlinearity. Applications to the complex Ginzburg–Landau equation are illustrated and several classes of uniformly translating solutions are obtained accordingly. Part of the work was announced at the International Conference on Complementarity, Duality, and Global Optimization in Science and Engineering, Virginia Tech. University, Blacksburg, Virginia, August 15–17, 2005. This work is supported by NSF Grant CCF–0514768.     

Microscopic Superconductivity and Room Temperature Electronics of High-Tc Cuprates

Abstract This paper points out that the Landau criterion for macroscopic superfluidity of He H is only a criterion for microscopic superfluidity of ^4He, extends the Landau criterion to microscopic superconductivity in fermions （electron and hole） system and system with Cooper pairs without long-range phase coherence. This paper gives another three non-superconductive systems that are of microscopic superconductivity. This paper demonstrates that one application of microscopic superconductivity is to establish room temperature electronics of the high-To cuprates.     

Edge agreement of second-order multi-agent system with dynamic quantization via the directed edge Laplacian

This work explores the edge agreement problem of second-order multi-agent systems with dynamic quantization under directed communication. To begin with, by virtue of the directed edge Laplacian, we propose a model reduction representation of the closed-loop multi-agent system depending on the spanning tree subgraph. Considering the limitations of the finite bandwidth channels, the quantization effects of second-order multi-agent systems under directed graph are considered. The static quantizers generally contain a fixed quantization interval and infinite quantization level, which are, to some extent, inefficient and impractical. To further reduce the bit depth (number of bits available) and to obtain better precision, the dynamic quantized communication strategy referring to zooming in-zooming out scheme is required. Based on the reduced model associated with the essential edge Laplacian, the asymptotic stability of second-order multi-agent systems under dynamic quantized effects with only finite quantization level can be guaranteed. Finally, the simulation of altitude alignment of micro air vehicles is provided to verify the theoretical results.