On the Spectral Dimension of Causal Triangulations

We introduce an ensemble of infinite causal triangulations, called the uniform infinite causal triangulation, and show that it is equivalent to an ensemble of infinite trees, the uniform infinite planar tree. It is proved that in both cases the Hausdorff dimension almost surely equals 2. The infinite causal triangulations are shown to be almost surely recurrent or, equivalently, their spectral dimension is almost surely less than or equal to 2. We also establish that for certain reduced versions of the infinite causal triangulations the spectral dimension equals 2 both for the ensemble average and almost surely. The triangulation ensemble we consider is equivalent to the causal dynamical triangulation model of two-dimensional quantum gravity and therefore our results apply to that model.     

尿素和尿素—Fe配位化合物的晶格振动光谱研究

采用直接固相反应将尿素与氯化铁(摩尔比6∶1)混合,经充分研磨合成了尿素铁盐配位化合物,并对其拉曼光谱和红外吸收光谱进行了研究。由于金属原子的影响,尿素分子的一些特征振动频率发生了变化:CO伸缩振动和NH2的对称弯曲振动的频率下降;而CN伸缩振动和NH2反对称弯曲振动的频率增加。对尿素以及尿素—Fe(III)的晶格振动模进行了识别。研究结果表明:Fe与尿素中的氧原子发生了配合而形成配位物。     

Dynamics of Triangulations

We study a few problems related to Markov processes of flipping triangulations of the sphere. We show that these processes are ergodic and mixing, but find a natural example which does not satisfy detailed balance. In this example, the expected distribution of the degrees of the nodes seems to follow the power law d ⁻⁴.     

Lattice Properties of Ring-like Quantum Logics

Generalized Boolean quasirings (GBQRs) are extensions of partial algebras thatare in one-to-one correspondence to bounded lattices with an involutoryantiautomorphism. This correspondence generalizes the bijection betweenBoolean rings and Boolean algebras and provides for a large variety of presumptivequantum logics (including logics which can be defined by means of Mackey'sprobability function). It is shown how properties of the corresponding latticesare reflected in GBQRs and what the implications are of the associativity of the+-operation of GBQRs, which can be interpreted as some kind of an exclusiveor-operation. We prove that under very weak conditions, which, however, seemto be essential for experimental verifications, the associativity of + implies theclassicality of the considered quantum mechanical system.     

BRST Quantization of Unimodular Gravity

We study the quantization of two versions of unimodular gravity, namely fully diffeomorphism-invariant unimodular gravity and unimodular gravity with fixed metric determinant, utilizing standard path integral approach. We derive the BRST symmetry of effective actions corresponding to several relevant gauge conditions. We observe that for some gauge conditions, the restricted gauge structure may complicate the formulation and effective actions, in particular, if the chosen gauge conditions involve the canonical momentum conjugate to the induced metric on the spatial hypersurface. The BRST symmetry is extended further to the finite field-dependent BRST transformation, in order to establish the mapping between different gauge conditions in each of the two versions of unimodular gravity.     

Spectral Energy Density of Phonons in Metals with Cubic Lattice

Russian Physics Journal - An expression is given for the spectral energy density of acoustic phonons. The basic properties of anharmonic phonons are introduced, and an expression is written for...     

Spectral Properties of Hypoelliptic Operators

 We study hypoelliptic operators with polynomially bounded coefficients that are of the form K=∑ _i=1 ^m X _i ^T X _i +X ₀+f, where the X _j denote first order differential operators, f is a function with at most polynomial growth, and X _i ^T denotes the formal adjoint of X _i in L ². For any ɛ>0 we show that an inequality of the form ||u||_δ,δ≤C(||u||_0,ɛ+||(K+iy)u||_0,0) holds for suitable δ and C which are independent of yR, in weighted Sobolev spaces (the first index is the derivative, and the second the growth). We apply this result to the Fokker-Planck operator for an anharmonic chain of oscillators coupled to two heat baths. Using a method of Hérau and Nier [HN02], we conclude that its spectrum lies in a cusp {x+iy|x≥|y|^τ−c,τ(0,1],cR}. Received: 30 July 2002 / Accepted: 18 October 2002 Published online: 25 February 2003 RID="*" ID="*" Present address: Mathematics Research Centre of the University of Warwick Communicated by A. Kupiainen     

Skew Young Diagram Method in Spectral Decomposition of Integrable Lattice Models

The spectral decomposition of the path space of the vertex model associated to the vector representation of the quantized affine algebra is studied. We give a one-to-one correspondence between the spin configurations and the semistandard tableaux of skew Young diagrams. As a result we obtain a formula of the characters for the degeneracy of the spectrum in terms of skew Schur functions. We conjecture that our result describes the -module contents of the Yangian -module structures of the level 1 integrable modules of the affine Lie algebra . An analogous result is obtained also for a vertex model associated to the quantized twisted affine algebra , where characters appear for the degeneracy of the spectrum. The relations to the spectrum of the Haldane-Shastry and the Polychronakos models are also discussed. Received: 28 July 1996 / Accepted: 11 October 1996     

Uniform Infinite Planar Triangulations

The existence of the weak limit as n of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random triangulations of the plane.     

双参数自适应格形滤波器的随机收敛特性

本文用矩阵特征值摄动理论、算子谱范数和不动点原理研究了双参数自适应格形滤波器的随机特性。双参数相对差值‖△_n,t‖是重要的因子。得到如下结论:1.元算子均值的奇值在半径正比于‖△_n,t‖的圆内变化,‖△_n,t‖不但改变奇值的大小,还改变它的方向;2.元算子均方值的特征值在半径正比于‖△_n,t‖的圆内变化;3.步距β_m的取值比单参数的情形更为严格;4.不存在零失调,它在以单参数时的失调为中心,长度正比于‖△_n,t‖的区间内变化;5.失调与阶数N的关系既不是线性的,也不是指数的,基本上介于两者之间;6.确定性信号的收敛速率慢于不相关信号的速率。     

A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations

Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated.     

A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations

Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated.     

Growth of Uniform Infinite Causal Triangulations

We introduce a growth process which samples sections of uniform infinite causal triangulations by elementary moves in which a single triangle is added. A relation to a random walk on the integer half line is shown. This relation is used to estimate the geodesic distance of a given triangle to the rooted boundary in terms of the time of the growth process and to determine from this the fractal dimension. Furthermore, convergence of the boundary process to a diffusion process is shown leading to an interesting duality relation between the growth process and a corresponding branching process.     

Spectral Properties of Burgers and KPZ Turbulence

This paper presents the higher-order spectral densities of non-Gaussian random fields arising as scaling limits in the Burgers and KPZ turbulence problems with strongly dependent non-Gaussian initial conditions.     

偶氮连苯三酚试剂的合成及其光谱特性

合成了 2 -羧基苯胺重氮盐和 2 -羟基苯胺重氮盐 ,它们与连苯三酚偶联 ,得到新的偶氮试剂 4 - (2 -羧基苯偶氮 ) -连苯三酚和 4 - (2 -羟基苯偶氮 ) -连苯三酚。研究了偶氮试剂的红外光谱、紫外光谱和荧光光谱特性。     

Superior Mechanical Properties of GaAs Driven by Lattice Nanotwinning

Gallium arsenide(GaAs),a typical covalent semiconductor,is widely used in the electronic industry,owing to its superior electron transport properties.However,its brittle nature is a drawback that has so far significantly limited its application.An exploration of the structural deformation modes of GaAs under large strain at the atomic level,and the formulation of strategies to enhance its mechanical properties is highly desirable.The stressstrain relations and deformation modes of single-crystal and nanotwinned GaAs under various loading conditions are systematically investigated,using first-principles calculations.Our results show that the ideal strengths of nanotwinned GaAs are 14% and 15% higher than that of single-crystal GaAs under pure and indentation shear strains,respectively,without producing a significantly negative effect in terms of its electronic performance.The enhancement in strength stems from the rearrangement of directional covalent bonds at the twin boundary.Our results offer a fundamental understanding of the mechanical properties of single crystal GaAs,and provide insights into the strengthening mechanism of nanotwinned GaAs,which could prove highly beneficial in terms of developing reliable electronic devices.     

Spectral Properties of Amphiflavins in Polymer Matrices

The parameters characterizing the absorption, fluorescence and phosphorescence of 10-dodecylisoalloxazine (DIA), 10-octadecylisoalloxazine (OIA) 3-methyl-10-dodecylisoalloxazine (MDIA) embedded into polymeric matrices (polystyrene – PS, polymethacrylate methyl – PMM and poly(vinyl alcohol) – PVA) were studied. It was found that both the polarity of microenvironment and its structure influenced the changes of the spectral properties of the examined amphiflavins.