The fractional quantum Hall effect: Chern-Simons mapping,duality, Luttinger liquids and the instanton vacuum

We derive, from first principles, the complete Luttinger liquid theory of abelian quantum Hall edge states. This theory includes disorder and Coulomb interactions as well as the coupling to external electromagnetic fields. We introduce a theory of spatially separated edge modes, find an enlarged dual symmetry and obtain a complete classification of quasiparticle operators and tunneling exponents. The chiral anomaly on the edge is used to obtain unambiguously the Hall conductance. In resolving the problem of counter-flowing edge modes, we find that the long range Coulomb interactions play a fundamental role. In order to set up a theory for arbitrary ν we use the idea of a two-dimensional network of percolating edge modes. We derive an effective, single mode Luttinger liquid theory for tunneling processes into the edge which yields a continuous tunneling exponent 1/ν. The network approach is also used to re-derive the instanton vacuum theory for plateau transitions.     

Conformal field theory interpretation of black hole quasinormal modes

We obtain exact expressions for the quasinormal modes of various spin for the Ba?ados-Teitelboim-Zanelli black hole. These modes determine the relaxation time of black hole perturbations. Exact agreement is found between the quasinormal frequencies and the location of the poles of the retarded correlation function of the corresponding perturbations in the dual conformal field theory. This then provides a new quantitative test of the anti-de Sitter/conformal field theory correspondence.     

用等效矩形波导近似研究双模椭圆芯光纤的特性

用等效矩形波导近似，结合一级微扰理论，研究了双模椭圆芯光纤的传播特性，得到了双模运行的Ｖ值范围和Ｅｘ２１模与Ｅｘ１１模之间的双折射、模间色散随归一化频率和椭圆比的变化关系曲线     

R-Charged Black Hole and Holographic Superfluid

In this paper we consider an interesting model of superfluid and use AdS/CFT correspondence to extract sound modes. We assume that dual picture of superfluid is the R-charged black hole with two equal charges. By using hydrodynamic variables of such a black hole we obtain first, second and fourth sound modes as a function of black hole charge.     

Communication modes in scalar diffraction

The communication modes are a useful concept in studies of optical resolution, wave propagation, and image synthesis. We present an overview of earlier results on the communication modes in scalar diffraction theory. Besides the general theory, the modes are reviewed for the far-field and Fresnel regimes, and new eigenequations are derived for wide-angle diffraction. We prove a conjugate relationship between the transmitting and receiving modes in a general symmetric system. We also suggest an approximate method for far-field and Fresnel domain propagation, in which propagation amounts to a rotation of each mode in the complex plane. The main focus is on the near-field communication modes, where we present numerical examples of the modes and coupling strengths for a near-field geometry with a sub-wavelength size receiving domain. These results provide insights, for example, into the understanding of near-field scanning probe techniques.     

Topological Aspects of Superconductors at Dual Point

We study the properties of the Ginzburg-Landau model at the dual point for the superconductors. By making use of the U（1） gauge potential decomposition and the φ-mapping theory, we investigate the topological inner structure of the Bogomol＇nyi equations and deduce a modified decoupled Bogomol＇nyi equation with a nontrivial topological term, which is ignored in conventional model. We find that the nontrivial topological term is closely related to the N-vortex, which arises from the zero points of the complex scalar field, Furthermore, we establish a relationship between Ginzburg Landau free energy and the winding number.     

Complex Chiral Bosons and Their Weyl Fermionic Representation

The complex chiral boson model is proposed. We quantize the theory by using Dirac algorithm and discuss the BRST aspects of the complex chiral boson theory. It is also shown that at the quantum level the theory can be expressed in terms of a Weyl fermionic representation. This suggests that the chiral bosons and Weyl fermions in two dimensions be equivalent in their dual form.     

Complex coupled-mode theory for tapered optical waveguides

A coupled-mode formulation based on complex local modes is developed for tapered and longitudinally varying optical waveguides. Different from the conventional coupled-mode theory that requires integration over the entire spectrum of radiation modes, the new formulation treats the radiation fields via discrete complex modes similarly to the guided modes. Accuracy, convergence, and scope of validity for the solutions of the complex coupled-mode equations are investigated in detail for a typical single-mode waveguide taper. It is demonstrated that the complex coupled-mode theory has overcome the difficulties of the conventional theory in simulation of radiation field effects while preserving the simplicity and intuitiveness of this popular method.     

Dynamics of transients in yttrium-iron-garnet

Yttrium-iron-garnet (YIG) is an important technological material used in microwave devices. In this paper we use dual microwave (1-4 GHz) drives to study the dynamical bifurcation behavior of magnetostatic and spin-wave modes in YIG spheres and rectangular films. The samples are placed in a dc magnetic field and driven by cw and pulse-modulated microwave excitations at magnetostatic mode frequencies. A second microwave drive applied to the sample excites additional spin-wave modes that can interact with those arising from the original excitation and thereby affect the transmission characteristics at the primary frequency. We find a significant decrease in transmission of the primary when the secondary frequency is tuned to approximately half that of the primary drive. This decrease is observed both in the steady state behavior and in the initial overshoot transient associated with pulse modulation of the primary excitation. Results such as these are often treated by extending linear theory to include higher order interaction terms. Herein we present a simple dynamical model that reproduces results that qualitatively resemble the experimental data. (c) 1997 American Institute of Physics.     

Tree-level recursion relation and dual superconformal symmetry of the ABJM theory

We propose a recursion relation for tree-level scattering amplitudes in three-dimensional Chern-Simons-matter theories. The recursion relation involves a complex deformation of momenta which generalizes the BCFW-deformation used in higher dimensions. Using background field methods, we show that all tree-level superamplitudes of the ABJM theory vanish for large deformations, establishing the validity of the recursion formula. Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. Using generalized unitarity methods, we extend this symmetry to the cut-constructible parts of the loop amplitudes.     

Quantum field theoretical description of unstable behavior of a Bose-Einstein condensate with a highly quantized vortex in a harmonic potential

The Bogoliubov-de Gennes equations are used for a number of theoretical works to describe quantum and thermal fluctuations of trapped Bose-Einstein condensates. We consider the case in which the condensate has a highly quantized vortex. It is known that these equations have complex eigenvalues in this case. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugates to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings the operators associated with the complex modes, which are simply neither bosonic nor fermionic ones. The eigenstate of the Hamiltonian is given. Introducing the notion of the physical states, we discuss the instability of the condensates in the context of Kubo’s linear response theory.     

Bosonic topological insulator intermediate state in the superconductor-insulator transition

A low-temperature intervening metallic regime arising in the two-dimensional superconductor-insulator transition challenges our understanding of electronic fluids. Here we develop a gauge theory revealing that this emergent anomalous metal is a bosonic topological insulator where bulk transport is suppressed by mutual statistics interactions between out-of-condensate Cooper pairs and vortices and the longitudinal conductivity is mediated by symmetry-protected gapless edge modes. We explore the magnetic-field-driven superconductor-insulator transition in a niobium titanium nitride device and find marked signatures of a bosonic topological insulator behavior of the intervening regime with the saturating resistance. The observed superconductor-anomalous metal and insulator-anomalous metal dual phase transitions exhibit quantum Berezinskii-Kosterlitz-Thouless criticality in accord with the gauge theory.     

Non-universal shear viscosity from Einstein gravity

A very famous result of gauge/gravity duality is the universality of the ratio of shear viscosity to entropy density in every field theory holographically dual to classical, two-derivative (Einstein) gravity. We present a way to obtain deviation from this universality by breaking the rotational symmetry spontaneously. In anisotropic fluids additional shear modes exist and their corresponding shear viscosities may be non-universal. We confirm this by explicitly calculating the shear viscosities in a transversely isotropic background, a p-wave superfluid, and study its critical behavior. This is a first decisive step towards further applications of gauge/gravity duality to physical systems.     

Quantum field theoretical analysis on unstable behavior of Bose-Einstein condensates in optical lattices

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows an unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consistent with those given by the discrete nonlinear Schrödinger equation.     

On the glueball spectrum of walking backgrounds from wrapped-D5 gravity duals

We compute the mass spectrum of glueball excitations of a special class of strongly-coupled field theories via their Type-IIB supergravity dual. We focus on two subclasses of backgrounds, which have different UV-asymptotics, but both of which exhibit walking behavior, in the weak sense that the gauge coupling of the dual field theory exhibits a quasi-constant behavior at strong coupling over a range of energies, before diverging in the deep IR. We improve on earlier calculations, by making use of the fully rigorous treatment of the 5-dimensional consistent truncation, including the rigorous form of the boundary conditions. In both cases there is a parametrically light scalar glueball. In the first case, this is a physical state, while in the second case this result is unphysical, since the presence of higher-order operators in the dual field theory makes the whole (physical) spectrum depend explicitly on a (unphysical) UV cutoff scale.     

AdS 5 Solutions of Type IIB Supergravity and Generalized Complex Geometry

We use the formalism of generalized geometry to study the generic supersymmetric AdS ₅ solutions of type IIB supergravity that are dual to ${\mathcal{N}=1}We use the formalism of generalized geometry to study the generic supersymmetric AdS ₅ solutions of type IIB supergravity that are dual to N=1{\mathcal{N}=1} superconformal field theories (SCFTs) in d = 4. Such solutions have an associated six-dimensional generalized complex cone geometry that is an extension of Calabi-Yau cone geometry. We identify generalized vector fields dual to the dilatation and R-symmetry of the dual SCFT and show that they are generalized holomorphic on the cone. We carry out a generalized reduction of the cone to a transverse four-dimensional space and show that this is also a generalized complex geometry, which is an extension of K?hler-Einstein geometry. Remarkably, provided the five-form flux is non-vanishing, the cone is symplectic. The symplectic structure can be used to obtain Duistermaat-Heckman type integrals for the central charge of the dual SCFT and the conformal dimensions of operators dual to BPS wrapped D3-branes. We illustrate these results using the Pilch-Warner solution.     

Development of a dual cell, flow-injection sample holder, and NMR probe for comparative ligand-binding studies

NMR based ligand screening is becoming increasingly important for the very early stages of drug discovery. We have proposed a method that makes highly efficient use of a single sample of a scarce target, or one with poor or limited solubility, to screen an entire compound library. This comparative method is based on immobilizing the target for the screening procedure. In order to support the method, a dual cell, flow injection probe with a single receiver coil has been constructed. The flow injection probe has been mated to a single high performance pump and sample handling system to enable the automated analysis of large numbers of compound mixes for binding to the target. The probe, having an 8 mm 1H/2H dual tuned coil and triple axis gradients, is easily shimmed and yields NMR spectra of comparable quality to a standard 5 mm high-resolution probe. The lineshape in the presence of a solid support is identical to that in glass NMR tubes in a 5 mm probe. Control spectra of each cell are identical and well separated, while ligand binding in a complex mixture can be readily detected in 20-30 min, thus paving the way for use of the probe for actual drug discovery efforts.     

Exotic Tensor Gauge Theory and Duality

 Gauge fields in exotic representations of the Lorentz group in D dimensions – i.e. ones which are tensors of mixed symmetry corresponding to Young tableaux with arbitrary numbers of rows and columns – naturally arise through massive string modes and in dualising gravity and other theories in higher dimensions. We generalise the formalism of differential forms to allow the discussion of arbitrary gauge fields. We present the gauge symmetries, field strengths, field equations and actions for the free theory, and construct the various dual theories. In particular, we discuss linearised gravity in arbitrary dimensions, and its two dual forms. Received: 9 September 2002 / Accepted: 22 October 2002 Published online: 21 February 2003 Communicated by A. Connes     

Dual Space Analyzing Based on Symmetry Properties for Phonons of Si Quantum Dot

Phonon modes in spherical Si quantum dots (QDs) with up to 7.9 nm in diameter are calculated by using the projection operators of the group theory into valence force field model. The phonons of dot modes in each of five irreducible representations (symmetries) are classified by using a dual space analysis method. It is found that the bulk-like modes with localization radius much smaller than the dot‘s radius have clearly pronounced bulk specific-κdefinite bulk band (one in six modes). In Si dots of all sizes, each specific bulk-like dot mode has specific symmetry.TO dot modes and bulk-like X-derived TA and LA dot modes red-shift in frequency with decreasing dot size. There is almost not LO/TO mixing for bulk-like modes. As for the surface-like modes localized at the periphery of the dot,their eigenmodes have not a dominant bulk specific-κ point parentage or a dominant BZ parentage around some special point. They are a superposition of many bulk bands with κ from all over the bulk BZ. They have much significant mode mixing than the bulk-like phonons. The classification of dot modes based on the symmetry of group theory will bring advantageous to the discussion of Ramam spectrum, electron-phonon interaction and other phonon-assisted effects in QDs.