Hölder Regularity of Integrated Density of States for the Almost Mathieu Operator in a Perturbative Regime

Consider the Almost Mathieu operator H = cos 2(k +)+ on the lattice. It is shown that for large , the integrated density of states is Hölder continuous of exponent < . This result gives a precise version in the perturbative regime of recent work by M. Goldstein and W. Schlag on Hölder regularity of the integrated density of states for 1D quasi-periodic lattice Schrödinger operators, assuming positivity of the Lyapunov exponent (and proven by different means). Our approach provides also a new way to control Green's functions, in the spirit of the author's work in KAM theory. It is by no means restricted to the cosine-potential and extends to band operators.     

The coherent-constructible correspondence and Fourier-Mukai transforms

As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on ℝ ⁿ . In this paper we investigate and reprove some of Kawamata’s results from this perspective.     

Non Equilibrium Current Fluctuations in Stochastic Lattice Gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation j of the empirical current with a rate functional I(j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional I. We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.     

表面人工低维结构的功能设计与构造

可控地构造具有一定功能的表面人工低维结构,并且总结、理解体系微观结构对其宏观性质影响的一般规律,不仅对探索低维基本物理以及其中的新奇量子现象至关重要,更是微电子工业保持持续发展的关键前提.这方面的研究包括发展新的生长技术实现对体系形成过程的精确控制,对获得的材料做高分辨率的表征;从理论上则要理解体系的生长过程,阐明热力学、动力学的作用机理,从而指导制备技术的发展.深入研究表面人工低维结构的性质更可能导致新物理现象与原理的发现,产生全新的器件概念,进一步反馈给体系功能的设计,推动基础研究与应用探索的发展.文章简要介绍了表面物理国家重点实验室近年来在表面人工低维结构的功能设计与构造方面的研究成果     

The number of electronic states in metallic nanowires as a function of the electrochemical potential

We derive a mathematical expression for the number of electronic states in metallic nanowires within the electrochemical environment as a function of the electrochemical potential so that the variation of the above number with respect to this potential is discussed within an electron energy range from zero energy up to Fermi energy.     

Efficient Generation of Atomic Singlet State with Rydberg Blockade and Lie-Transform-Based Pulse Design

A protocol to generate atomic singlet state of three atoms is proposed. The strong Rydberg interactions between atoms mediate the multi-qubit operations and help to simplify the dynamics of the system. The effective Hamiltonian is constructed in the regime of Rydberg blockade and the evolution path is built up from an initial state to the target singlet state via the Lie-transform-based pulse design. Numerical simulations show the protocol can produce atomic singlet state with high fidelity and holds robustness against several types of experimental imperfections. Therefore, it may provide some useful results for the generation of singlet states in atomic system.     

Seeing the Unseen: Experimental Observation of Magnetic Anapole State Inside a High-Index Dielectric Particle

The existence of non-radiating electromagnetic sources attracts much attention in photonic community and gives rise to extensive discussions of various applications in lasing, medical imaging, sensing, and nonlinear optics. In this article, the existence of magnetic anapole states (or magnetic-type non-radiating sources) characterized by a suppressed magnetic dipole radiation in a dielectric cylindrical particle is theoretically predicted and experimentally demonstrated. The specific features of the magnetic anapole state under ideal conditions are identified, followed by a demonstration of how their existence can be detected in practical structures. The concept is valid in various frequency bands from visible range for nanoparticles to microwave range for millimeter size objects. The experimental study is performed in microwave frequency range which allows not only to measure the far-field (scattered field) characteristics, but also to probe the peculiar field profile directly inside the dielectric particle. The experimental results agree well with the analytical ones and pave the way to detect and identify nontrivial different-type anapole states.     

On the equation of state of classical one-component systems with long-range forces

Several definitions of the pressure are introduced for one-component systems and shown to be nonequivalent in the presence of a rigid neutralizing background. Relations between these pressures are derived for finite and infinite systems; these relations depend on the asymptotic behavior of the force at infinity, with the Coulomb force at the borderline between different properties. It is argued that only one of those definitions is physically acceptable and its properties are discussed in relation to the asymptotic behavior of the force. It is seen in particular that a knowledge of the state of the infinite system is not sufficient to determine its thermodynamic properties. The results are illustrated by some typical examples.For example, for two-dimensional systems with three-dimensional Coulomb interaction see refs. 2–4.     

Propagation of a decentered astigmatic partially coherent beam in a turbulent atmosphere

Propagation properties of a decentered general astigmatic partially coherent beam (i.e., decentered twisted anisotropic Gaussian Schell-model beam) in a turbulent atmosphere are investigated. Analytical formulas for the cross-spectral density and decentered parameter of a decentered astigmatic partially coherent beam propagating in a turbulent atmosphere are derived. Irradiance properties of a decentered astigmatic partially coherent beam in a turbulent atmosphere are studied graphically, and are found to be quite different from its properties in free space.