Nucleation of Instability of the Meissner State of 3-Dimensional Superconductors

This paper concerns a nonlinear partial differential system in a 3-dimensional domain involving the operator curl², which is a simplified model used to examine nucleation of instability of the Meissner state of a superconductor as the applied magnetic field reaches the superheating field. We derive a priori C ^2+α estimates for a weak solution H, the curl of the magnetic potential, and determine the location of the maximal points of |curlH| which correspond to the nucleation of instability of the Meissner state. We show that, if the penetration length is small, the solution exhibits a boundary layer. If the applied magnetic field is homogeneous, |curlH| is maximal around the points on the boundary where the applied field is tangential to the surface.     

Neumann resonances in linear elasticity for an arbitrary body

We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle inR ³ with Neumann boundary conditions. We prove that there exists a sequence of resonances tending rapidly to the real axis.Partly supported by BSF under grant MM 401.     

A general finite difference time domain method for hybrid dispersive media model

The shift operator finite difference time domain (SO-FDTD) method is developed to deal with a hybrid dispersive media model. First, we prove that the complex permittivity of the hybrid dispersive media model can be described by a rational polynomial fraction with respect to jω. Then, the relation between electric displacement D and electric field strength E is derived in the time domain by introducing z_t as a shift operator. The constitutive relation in the discretized time domain and the recursive formulation of D and E available for FDTD computation are obtained. Finally, the reflection of the hybrid dispersive slab is computed. The computed results are in good agreement with that obtained by analytic method. This illustrates the generalization and the feasibility of the presented scheme.     

一种处理色散介质问题的通用时域有限差分方法

色散介质的介电系数是频率的函数,使本构关系在时域成为卷积关系.这就给用时域有限差分方法计算色散介质中波的散射和传播带来了困难.现有算法往往要针对不同色散介质模型推导相应的递推公式,算法的通用性较差.本文完善和发展了移位算子-时域有限差分方法,使之成为一种处理色散介质电磁问题的通用方法.首先,证明了常见的三种色散介质模型(德拜模型、洛伦兹模型和德鲁模型)的介电系数均可以写成适于移位算子法计算的有理分式函数形式.然后,用/t代替jω,过渡到时域,再引入时域移位算子z_t代替时间微分算子来处理有理分式函数形式的介电系数,给出离散时域本构关系的表示式,进而导出时域有限差分方法当中电位移矢量和电场强度之间的关系.最后,计算了几种色散介质的电磁散射,数值结果表明了本文方法和程序的通用性和正确有效性. 关键词： 时域有限差分方法 色散介质 移位算子     

一种色散介质FDTD通用吸收边界

由单轴各向异性介质所满足的场方程出发,并根据相位匹配原理以得到介质中的色散关系和无反射条件.结合频域到时域的转换关系（即用/t代替jω）和移位算子时域有限差分（SO-FDTD）方法提出了一种适用于各向同性常见色散介质模型,包括德拜模型、洛伦兹模型、德鲁德模型等的通用UPML吸收边界.数值结果表明了该算法的通用性和高效性. 关键词： 时域有限差分 吸收边界 移位算子 色散介质     

Geometric conservation law and applications to high-order finite difference schemes with stationary grids

The geometric conservation law (GCL) includes the volume conservation law (VCL) and the surface conservation law (SCL). Though the VCL is widely discussed for time-depending grids, in the cases of stationary grids the SCL also works as a very important role for high-order accurate numerical simulations. The SCL is usually not satisfied on discretized grid meshes because of discretization errors, and the violation of the SCL can lead to numerical instabilities especially when high-order schemes are applied. In order to fulfill the SCL in high-order finite difference schemes, a conservative metric method (CMM) is presented. This method is achieved by computing grid metric derivatives through a conservative form with the same scheme applied for fluxes. The CMM is proven to be a sufficient condition for the SCL, and can ensure the SCL for interior schemes as well as boundary and near boundary schemes. Though the first-level difference operators δ₃ have no effects on the SCL, no extra errors can be introduced as δ₃ = δ₂. The generally used high-order finite difference schemes are categorized as central schemes (CS) and upwind schemes (UPW) based on the difference operator δ₁ which are used to solve the governing equations. The CMM can be applied to CS and is difficult to be satisfied by UPW. Thus, it is critical to select the difference operator δ₁ to reduce the SCL-related errors. Numerical tests based on WCNS-E-5 show that the SCL plays a very important role in ensuring free-stream conservation, suppressing numerical oscillations, and enhancing the robustness of the high-order scheme in complex grids.     

A theoretical analysis of the magnetic properties of La<Subscript>2</Subscript>CuO<Subscript>4</Subscript>

The magnetic properties of the La₂CuO₄ are analyzed by means of the paramagnetic solution of the Hubbard model within the composite operator method. The experimental findings of the inelastic neutron magnetic scattering [R. Coldea et al., Phys. Rev. Lett. 86, 5377 (2001)] for the spin spectrum, the spin-wave intensity and the behavior of the dispersion at the zone boundary are well described by our results although the difference in phase. The Hubbard model emerges has a minimal model capable to describe the anomalous magnetic behavior of such a strongly correlated material. Received 29 July 2002 / Received in final form 2 January 2003 Published online 14 March 2003     

Gravity and the Noncommutative Residue for Manifolds with Boundary

We prove a Kastler–Kalau–Walze type theorem for the Dirac operator and the signature operator for 3,4-dimensional manifolds with boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action in the case of 4-dimensional manifolds with flat boundary.      

Number-Phase Quantization Scheme and the Quantum Effects of a Mesoscopic Electric Circuit at Finite Temperature

For L-C circuit, a new quantized scheme has been proposed in the context of number-phase quantization. In this quantization scheme, the number n of the electric charge q(q=en) is quantized as the charge number operator and the phase difference θ across the capacity is quantized as phase operator. Based on the scheme of number-phase quantization and the thermo field dynamics (TFD), the quantum fluctuations of the charge number and phase difference of a mesoscopic L-C circuit in the thermal vacuum state, the thermal coherent state and the thermal squeezed state have been studied. It is shown that these quantum fluctuations of the charge number and phase difference are related to not only the parameters of circuit, the squeezing parameter, but also the temperature in these quantum states. It is proven that the number-phase quantization scheme is very useful to tackle with quantization of some mesoscopic electric circuits and the quantum effects.     

On the Evaluation of the Evolution Operator Z Reg( R 2, R 1) in the Diakonov–Petrov Approach to the Wilson Loop

We evaluate the evolution operator Z _Reg(R ₂,R ₁) introduced by Diakonov and Petrov for the definition of the Wilson loop in terms of a path integral over gauge degrees of freedom. We use the procedure suggested by Diakonov and Petrov (Physics Letters B 224 (1989) 131) and show that the evolution operator vanishes. PACS numbers: 11.10.-z; 11.15.-q; 12.38.-t; 12.38.Aw; 12.90.+b.     

Exact ground-state for the periodic Anderson model in dimensions at finite value of the interaction and absence of the direct hopping in the correlated f-band

We report for the first time exact ground-states deduced for the D = 2 dimensional generic periodic Anderson model at finite U, the Hamiltonian of the model not containing direct hopping terms for f-electrons ( t ^f = 0). The deduced itinerant phase presents non-Fermi liquid properties in the normal phase, emerges for real hybridization matrix elements, and not requires anisotropic unit cell. In order to deduce these results, the plaquette operator procedure has been generalised to a block operator technique which uses blocks higher than an unit cell and contains f-operator contributions acting only on a single central site of the block. Received 1st July 2002 / Received in final form 16 September 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: gulacsi@heavy-ion.atomki.hu     

Conformal boundary state for the rectangular geometry

We discuss conformal field theories (CFTs) in rectangular geometries, and develop a formalism that involves a conformal boundary state for the 1+1d$1+1\mathrm{d}$ open system. We focus on the case of homogeneous boundary conditions (no insertion of a boundary condition changing operator), for which we derive an explicit expression of the associated boundary state, valid for any arbitrary CFT. We check the validity of our solution, comparing it with known results for partition functions, numerical simulations of lattice discretizations, and coherent state expressions for free theories.     

An improved operator expansion algorithm for direct and inverse scattering computations

Abstract

In the first part of the paper we present an implementation of Milder's operator expansion formalism for acoustic scattering from a rough non-periodic surface. Our main contribution to the forward-field calculation is the development of two accurate ways of computing the order-zero normal differentiation operator N ₀. The accuracy of our implementation is tested numerically. In the second part of our paper we apply this approach, combined with a continuation method, to an inverse scattering problem. The resulting scheme performs significantly better than the classical first-order methods.     

A Spin-Shift Operator of the Multi-particle Ruijsenaars–Schneider Hamiltonian

We obtain a spin-shift operator for the multi-particle trigonometric Ruijsenaars–Schneider Hamiltonian. This result is a generalization of the argument in Phys. Lett. B 375 (1996), 89–97, where the integrability of the one-particle Ruijsenaars–Schneider system is shown by using the existence of a spin-shift operator.     

An iterative solution of the rough-surface scattering problem

Abstract

An iterative solution to the problem of scattering from a one-dimensional rough surface is obtained for the Dirichlet boundary condition. The advantages of this method are that bounds for convergence of the solution can be established and that the solution may readily be iterated to sufficiently high order in the interaction to examine the rate at which it converges. Absolute convergence of the iterative solution is also a sufficient condition for the convergence of the operator expansion method for surfaces on which the slope is everywhere less than unity. A numerical example of scattering from an echelette grating is considered, and bounds for convergence established. It is found that for scattering from such surfaces the rate at which the iterative solution converges decreases as the surface slope is increased. Corresponding results are found for the operator expansion method.     

Generalized Operator Yang-Baxter Equations,Integrable ODEs and Nonassociative Algebras

Abstract

Reductions for systems of ODEs integrable via the standard factorization method (the Adler-Kostant-Symes scheme) or the generalized factorization method, developed by the authors earlier, are considered. Relationships between such reductions, operator Yang-Baxter equations, and some kinds of non-associative algebras are established.     

Detection of topological symmetry in the one-dimensional Affleck-Kennedy-Lieb-Tasaki model of integer spin with ultracold spinor atoms in optical lattices

A scheme is proposed for detection of the topology in the one-dimensional Afeck-Kennedy-Lieb-Tasaki model,based on ultracold spinor atomic gas in an optical lattice.For this purpose,a global operation O(θ)is introduced with respect to the breaking of spinrotational symmetry.Consequently,the topology can be manifested unambiguously by identifying the special values ofθwhere the expectation value of the global operator with degenerate ground states is vanishing.Furthermore,experimentallyθcan be detected readily by the interference of ultracold atomic gases.This scheme can be implemented readily in experiment since it does not need the addressing of individual atoms or the probing of a boundary.     

Singletons and logarithmic CFT in ADS/CFT correspondence

We discuss a possible relation between singletons in AdS space and logarithmic conformal field theories at the boundary of AdS. It is shown that the bulk Lagrangian for singleton field (singleton dipole) induces on the boundary the two-point correlation function for logarithmic pair. Bulk interpretation of mixing between logarithmic operator D and zero mode operator C under the scale transformation is discussed as well as some other issues.     

Repeated application of the recursion operator for a new hierarchy of negative-order integrable KdV equations

ABSTRACT

In this work we use the repeated application of the recursion operator to establish a new hierarchy of negative-order integrable KdV equations of higher orders. The concept of the inverse recursion operator allows us to develop this new hierarchy. The complete integrability of each equation is guaranteed via the use of the recursion operator. We show that the dispersion relations of this hierarchy follow an infinite geometric series. Multiple soliton solutions for each equation of the hierarchy are obtained.     

A Finite Dimensional Analog of the Krein Formula

Abstract

I offer a simple and useful formula for the resolvent of a small rank perturbation of large matrices. I discuss applications of this formula, in particular, to analytical and numerical solving of difference boundary value problems. I present examples connected with such problems for the difference Laplacian and estimate numerical efficiency of the corresponding algorithms.