Abstract:
The optical properties of slab waveguides made of indefinite permittivity ($\vep$) materials (IEM) are considered. In this medium the transverse permittivity is negative while the longitudinal permittivity is positive. At any given frequency the waveguide supports an infinite number of transverse magnetic (TM) eigenmodes. For a slab waveguide with a fixed thickness, at most only one TM mode is forward-wave. The rest of them are backward waves which can have very large phase index. At a critical thickness, the waveguide supports degenerate forward- and backward-wave modes with zero group velocity. Above the critical thickness, the waveguide supports complex-conjugate decay modes instead of propagating modes. The presence of loss in IEMs will lift the degeneracy, resulting in modes with finite group velocity. Feasible realization is proposed. The performance of IEM waveguide is analyzed and possible applications are discussed which are supported by numerical calculations. These slab waveguides can be used to make optical delay lines in optical buffers to slow down and trap light, to form open cavities, to generate strong longitudinal electric fields, and as phase shifters in optical integrated circuits.

Abstract:
We present a conjecture describing new long range correlations among the Riemann zeros leading to 3 principal features: (i) The spectral auto-correlation is invariant w.r.t. the averaging window. (ii) Resurgence occurs wherein the lowest zeros appear in all auto-correlations. (iii) Suitably defined correlations lead to predictions (prophecy) of new zeros. This conjecture is supported by analytical arguments and confirmed by numerical calculations using 10^{22} zeros computed by Odlyzko. The results lead to a self-duality of the Riemann spectrum similar to the quantum-classical duality observed in billiards.

Abstract:
We show that a metamaterial consisting of aligned metallic nanowires in a dielectric matrix has strongly anisotropic optical properties. For filling ratio f<1/2, the composite medium shows two surface plasmon resonances (SPRs): the transverse and longitudinal SPR with wavelengths lambda_tlambda_l, the longitudinal SPR, the material exhibits Re epsilon_l<0, Re epsilon_t>0, relative to the nanowires axis, enabling the achievement of broadband all-angle negative refraction and superlens imaging. An imaging theory of superlens made of these media is established. High performance systems made with Au, Ag or Al nanowires in nanoporous templates are designed and predicted to work from the infrared up to ultraviolet frequencies.

Abstract:
We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction, equivalent to an effective anisotropic refractive index n(theta). Imaging can be achieved with both negative (n<0) and positive (n>0) refractive indices. The Veselago-Pendry lens is a special case with isotropic negative refractive index of n(theta)=-1. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and requirements for sub-wavelength imaging are also presented.

Abstract:
We discuss the impact of recent developments in the theory of chaotic dynamical systems, particularly the results of Sinai and Ruelle, on microwave experiments designed to study quantum chaos. The properties of closed Sinai billiard microwave cavities are discussed in terms of universal predictions from random matrix theory, as well as periodic orbit contributions which manifest as `scars' in eigenfunctions. The semiclassical and classical Ruelle zeta-functions lead to quantum and classical resonances, both of which are observed in microwave experiments on n-disk hyperbolic billiards.

Abstract:
We systematically investigate the possibility of finding CP/T violation in the $\tau$ sector at Tau-Charm Factory. CP/T violation may occur at $\tau$ pair production process, expressed as electric dipole moment, and at $tau$ decay processes. By assuming that electric dipole moment as large as $10^{-19}$e-cm and CP/T violation effect orignating from $\tau$ decay as large as $10^{-3}$ are observable at Tau-Charm Factory, we studied all the possible extensions of the SM which are relevent for generating CP/T violation in $\tau$ sector. And we pointed there are a few kind of models, which are hopeful for generating such CP/T violation. For these models we consider all the theoretical and current experimental constraints and find that there exists some parameter space which will result in a measurable CP/T violation. Therefore we conclude that Tau-Charm Factory is a hopeful place to discover CP/T violation in $\tau$ sector.

Abstract:
We present a result relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. The result is supported by numerical computation of the resonances of the system of n disks on a plane. The result generalizes the Weyl law for the density of states of a closed system to chaotic open systems.

Abstract:
Trace analysis of radionuclides is an essential and versatile tool in modern science and technology. Due to their ideal geophysical and geochemical properties, long-lived noble gas radionuclides, in particular, 39Ar (t1/2 = 269 yr), 81Kr (t1/2 = 2.3x10^5 yr) and 85Kr (t1/2 = 10.8 yr), have long been recognized to have a wide range of important applications in Earth sciences. In recent years, significant progress has been made in the development of practical analytical methods, and has led to applications of these isotopes in the hydrosphere (tracing the flow of groundwater and ocean water). In this article, we introduce the applications of these isotopes and review three leading analytical methods: Low-Level Counting (LLC), Accelerator Mass Spectrometry (AMS) and Atom Trap Trace Analysis (ATTA).

Abstract:
An Ising model on the kagome lattice with super-exchange interactions is solved exactly under the presence of a nonzero external magnetic field. The model generalizes the super-exchange model introduced by Fisher in 1960 and is analyzed in light of a free-fermion model. We deduce the critical condition and present detailed analyses of its thermodynamic and magnetic properties. The system is found to exhibit a second-order transition with logarithmic singularities at criticality.

Abstract:
We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be observed in physical experiments through the auto-correlation of the transmission coefficient of waves in quantum billiards. Exact classical trace formulas of the resolvent are derived for the rectangle, equilateral triangle, and circle billiards. We also establish a correspondence between the classical periodic orbit length spectrum and the quantum spectrum for integrable polygonal billiards.