Boundary Scattering,Symmetric Spaces and the Principal Chiral Model on the Half-Line

We investigate integrable boundary conditions (BCs) for the principal chiral model on the half-line, and rational solutions of the boundary Yang-Baxter equation (BYBE). In each case we find a connection with (type I, Riemannian, globally) symmetric spaces G/H: there is a class of integrable BCs in which the boundary field is restricted to lie in a coset of H; these BCs are parametrized by G/H×G/H; there are rational solutions of the BYBE in the defining representations of all classical G parametrized by G/H; and using these we propose boundary S-matrices for the principal chiral model, parametrized by G/H×G/H, which correspond to our boundary conditions.An erratum to this article can be found at     

A duality theorem for the automorphism group of a covariant system

In this paper we examine the covariant representation theory of a covariant system (A, G) introduced by Doplicher, Kastler and Robinson. (A is aC*-algebra andG is a locally compact group of automorphisms ofA.) We define the concept of left tensor product of two covariant representations. Loosely stated, our duality theorem says thatG is canonically isomorphic to the set of bounded operator valued maps on the set of covariant representations of the covariant system (A, G) which preserve direct sums, unitary equivalence and left tensor products. We further show that the enveloping von Neumann algebraA(A, G) of the covariant system (A, G) admits a (not necessarily injective) comultiplicationd such that (A(A, G),d) is a Hopf von Neumann algebra. The intrinsic group of this Hopf von Neumann algebra is canonically isomorphic and (strong operator topology) homeomorphic toG.     

Group duality and the Kubo-Martin-Schwinger condition

We consider clusteringG-invariant states of aC*-algebraU endowed with an action of a locally compact abelian groupG. Denoting as usual byF _AB,G _AB, the corresponding two-point functions, we give criteria for the fulfillment of the KMS condition (w.r.t. some one-parameter subgroup ofG) based upon the existence of a closable mapT such thatTF _AB =G _AB for allA,BU. Closability is either inL (G),B(G), orC (G), according to clustering assumptions. Our criteria originate from the combination of duality results for the groupG (phrased in terms of functions systems), with density results for the two-point functions.Supported in part by the National Science Foundation     

On symmetries and averaging of the G-equation for premixed combustion

It is demonstrated that the G-equation for premixed combustion admits a diversity of symmetries properties, i.e. invariance characteristics under certain transformations. Included are those of classical mechanics such as Galilean invariance, rotation invariance and others. Also a new generalized scaling symmetry has been established. It is shown that the generalized scaling symmetry defines the physical property of the G-equation precisely. That is to say the value of G at a given flame front is arbitrary. It is proven that beside the symmetries of classical mechanics, particularly the generalized scaling symmetry uniquely defines the basic structure of the G-equation. It is also proven that the generalized scaling symmetry precludes the application of classical Reynolds ensemble averaging usually employed in statistical turbulence theory in order to avoid non-unique statistical quantities such as for the mean flame position. Finally, a new averaging scheme of the G-field is presented which is fully consistent with all symmetries of the G-equation. Equations for the mean G-field and flame brush thickness are derived and a route to consistent invariant modelling of other quantities derived from the G-field is illustrated. Examples of statistical quantities derived from the G-field both in the context of Reynolds-averaged models as well as subgrid-scale models for large-eddy simulations taken from the literature are investigated as to whether they are compatible with the important generalized scaling symmetry.     

Progress in Precise Measurements of the Gravitational Constant

The Newtonian gravitational constant G, which is one of the earliest fundamental constants introduced by human beings, plays an important role in cosmology, astrophysics, geophysics, metrology, and so on. In spite of the measurement of G having a relative longer history and more than 200 measurement results having been obtained during the past 200 years, G still remains the least precisely known among all fundamental physical constants up to now. Over the past three decades, many experimental physicists devoted themselves to the G measurement with various methods and resulted in a dozen precise values of G. However, the determined results are still in poor agreement with each other. A brief overview of the significance of the gravitational constant G is given herein, followed by an introduction into the history of G measurement. A summary of the five latest precise measurements performed during the past few years is presented. Finally, an outlook of the future development of G measurement is provided.     

An explicit *-product on the cotangent bundle of a Lie group

We give explicit formulas for a ^*-product on the cotangent bundle T ^* G of a Lie group G; these formulas involve on the one hand the multiplicative structure of the universal enveloping algebra U(G) of the Lie algebra G of G and on the other hand bidifferential operators analogous to the ones used by Moyal to define a ^*-product on IR²ⁿ.Chargé de recherches au FNRS, on leave of absence from Université libre de Bruxelles.     

一种计算金属剪切模量的本构模型：以Al为例

用两步法构建了一个与温度和压力相关的适用于金属材料的剪切模量本构模型,其中的第一步任务是求得沿0 K等温线上剪切模量随压力的变化规律,即求得G₁=G₁（P,0 K）的函数式.第二步是从0 K等温线上某一给定P的G值出发,求出沿等压线上剪切模量随温度T变化的规律,从而最终求得剪切模量本构模型G=G（P,T）的具体表达式.在这两个阶段的研究中都利用了超声波测量和第一性原理计算方法的研究结果.用铝为模型材料,对本模型的合理性进行了检验.结果表明,G的模型预测数据与试验测量及理论计算数据相比较,无论G的演化是沿冲击压缩轨迹、等熵压缩轨迹、等温压缩轨迹还是等压线轨迹,都能达到令人满意的程度,故可认为本模型具有良好的普适性和合理性. 关键词： 铝 本构模型 剪切模量 冲击波压缩     

Consequences of the complex character of the internal symmetry in supersymmetric theories

The consequences of the invariance of the superpotential under the complexificationG ^c of the internal symmetry group on the determination of the possible patterns of symmetry and supersymmetry breaking are established in a globally supersymmetric theory. In particular, in the case of global internal symmetry we show that a vacuum associaated to a pointz, whereG _z ^c G _z ^c is always degenerate with a vacuum associated to a pointz, whereG _z ^c =G _z ^c ; all the other degeneracies of the minimum of the potential on an orbit ofG ^c are also determined and shown to be completely removed when the internal symmetry is gauged. The zeroes of theD-term of a supersymmetric gauge theory are characterized as the points of the closed orbits ofG ^c which are at minimum distance from the origin; at these pointsG _z ^c =G _z ^c . It is rigorously proved that the minimum of the potential is zero if the gradient of the superpotential vanishes somewhere. It is also shown that theD-term necessarily vanishes at the minimum of the potential if the direction of spontaneous supersymmetry breaking is invariant byG.Partially supported by the Swiss National Science Foundation and INFN, Sezione di PadovaOn leave of absence from the Department of Physics of the University of Padova, Italy     

Degradation of the transconductance of gate-modulated generation current in nMOSFET

The degradation of transconductance (G) of gate-modulated generation current I_GD in LDD nMOSFET is investigated. The G curve shifts rightward under the single electron-injection-stress (EIS). The trapped electrons located in the gate oxide over the LDD region (Q_L) makes the effective drain voltage minish. Accordingly, the G peak in depletion (G_MD) and that in weak inversion (G_MW) decrease. It is found that Δ G_MD and Δ G_MW each have a linear relationship with the n-th power of stress time (tⁿ) in dual-log coordinate: Δ G_MD ∝ tⁿ, Δ G_MD ∝ tⁿ (n=0.25). During the alternate stress, the injected holes neutralize Q_L induced by the previous EIS. This neutralization makes the effective V_D restore to the initial value and then the I_GD peak recovers completely. Yet the threshold voltage recovery is incomplete due to the trapped electron located over the channel (Q_C). As a result, G_MW only recovers to the circa 50% of the initial value after the hole-injection-stress (HIS). Instead, G_MD is almost recovered. The relevant mechanisms are given in detail.     

Secondary order parameters in the structural phase transitions

In the Landau type phase transitions the primary order parameter is related with irreducible representation which subduces the high symmetry space groupG _o to the low symmetry space subgroupG andG _o G. We propose to define the secondary order parameters as irreducible representations which subduceG _o to the subgroupsH _l , whereH _l are simultaneously supergroups forG, i.e.G _o H _l G. From this statement general conclusions are drawn. In particular, for some phase transitions with elargement of the elementary cell, in addition to the superlattice reflections from the primary order parameter, the superlattice reflections from the secondary order parameters can arise in another non-equivalent high symmetry point of the reciprocal space.     

Determination of the gravitational constant G

A precise knowledge of the Newtonian gravitational constant G has an important role in physics and is of considerable meteorological interest. Although G was the first physical constant to be introduced and measured in the history of science, it is still the least precisely determined of all the fundamental constants of nature. The 2002 CODATA recommended value for G, G = (6.6742 ± 0.0010) × 10⁻¹¹m³ · kg⁻¹ · s⁻², has an uncertainty of 150 parts per million (ppm), much larger than that of all other fundamental constants. Reviewed here is the status of our knowledge of the absolute value of G, methods for determining G, and recent high precision experiments for determining G.     

Coincidence theorem for the direct correlation function of hard-particle fluids

The Mayerf-function for purely hard particles of arbitrary shape satisfiesf ²(1, 2)=–f(1, 2). This relation can be introduced into the graphical expansion of the direct correlation functionc(1, 2) to obtain a graphical expression for the case of exact coincidence, in position and orientation, of two identical hard cores. The resulting expression forc(1, 1)+1 contains only graphsG fromc(1), the sum of irreducible graphs with one labeled point. Relative to its coefficient inc(1),G occurs inc(1, 1) with an additional factorR _c which is 1 for the leading graph in the expansion and of the form 2–2L(G) for all other graphs. HereL(G)=0, 1, 2,..., is a nonnegative integer. Topological analysis is used to derive an expression forL(G) in terms of the connectivity properties ofG.     

The enveloping algebra of a covariant system

In an earlier work, Doplicher, Kastler and Robinson have examined a mathematical structure consisting of a pair (A, G), whereA is aC*-algebra andG is a locally compact automorphism group ofA. We call such a structure a covariant system. The enveloping von Neumann algebraA(A, G) of (A, G) is defined as a *-algebra of operator valued functions (called options) on the space of covariant representations of (A, G). The system (A, G) is canonically embedded in, and in fact generates, the von Neumann algebraA(A, G). Further we show there is a natural one-to-one correspondence between the normal *-representations ofA(A, G) and the proper covariant representations of (A, G). The relation ofA(A, G) to the covarainceC*-algebraC*(A, G) is also examined.     

RenormalizedG-convolution ofN-point functions in quantum field theory: Convergence in the Euclidean case II

The notion of Feynman amplitude associated with a graphG in perturbative quantum field theory admits a generalized version in which each vertexv ofG is associated with ageneral (non-perturbative)n _v -point functionH ⁿ _v , n_vdenoting the number of lines which are incident tov inG. In the case where no ultraviolet divergence occurs, this has been performed directly in complex momentum space through Bros-Lassalle'sG-convolution procedure.     

Operator Algebras and Poisson Manifolds¶Associated to Groupoids

It is well known that a measured groupoid G defines a von Neumann algebra W ^*(G), and that a Lie groupoid G canonically defines both a C ^*-algebra C ^*(G) and a Poisson manifold A ^*(G). We construct suitable categories of measured groupoids, Lie groupoids, von Neumann algebras, C ^*-algebras, and Poisson manifolds, with the feature that in each case Morita equivalence comes down to isomorphism of objects. Subsequently, we show that the maps G↦W ^*(G), G↦C ^*(G), and G↦A ^*(G) are functorial between the categories in question. It follows that these maps preserve Morita equivalence. Received: 6 December 2000 / Accepted: 19 April 2001     

On the Problem of the Amenability of the Gauge Group

Let G be one of the local gauge groups C(X, U(n)),C (X, U(n)), C(X, SU(n)) or C (X, SU(n)) where X is a compact Riemannian manifold. We observe that G has a nontrivial group topology, coarser than its natural topology, w.r.t. which it is amenable, viz. the relative weak topology of C(X, M(n)). This topology seems more useful than other known amenable topologies for G. We construct a simple fermionic model containing an action of G, continuous w.r.t. this amenable topology.     

Analytical studies on the Benney–Luke equation in mathematical physics

The enhanced (G′/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney–Luke equation by using the enhanced (G′/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper.     

Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G

We developed a gravity-gradiometer based on atom interferometry for the determination of the Newtonian gravitational constant G. The apparatus, combining a Rb fountain, Raman interferometry and a juggling scheme for fast launch of two atomic clouds, was specifically designed to reduce possible systematic effects. We present instrument performances and preliminary results for the measurement of G with a relative uncertainty of 1%. A discussion of projected accuracy for G measurement using this new scheme shows that the results of the experiment will be significant to discriminate between previous inconsistent values.     

Note on the natural system of units

We propose to substitute Newton’s constant G _N for another constant G ₂, as if the gravitational force would fall off with the 1/r law, instead of the 1/r ²; so we describe a system of natural units with G ₂, c and ℏ. We adjust the value of G ₂ so that the fundamental length L = L _Pl is still the Planck’s length and so G _N = L × G ₂. We argue for this system as (1) it would express longitude, time and mass without square roots; (2) G ₂ is in principle disentangled from gravitation, as in (2 + 1) dimensions there is no field outside the sources. So G ₂ would be truly universal; (3) modern physics is not necessarily tied up to (3 + 1)-dim. scenarios and (4) extended objects with p = 2 (membranes) play an important role both in M-theory and in F-theory, which distinguishes three (2, 1) dimensions. As an alternative we consider also the clash between gravitation and quantum theory; the suggestion is that non-commutative geometry [x _i , x _j ] = Λ² θ _ij would cure some infinities and improve black hole evaporation. Then the new length Λ shall determine, among other things, the gravitational constant G _N.     

Photoconductivity derived from an exact modelling of the uncompensated one-donor model. II—computer simulation of the steady-state exact model

Abstract

Stationary photoconductivity is treated with the model of Part I, free from any of the usual simplifying approximations of the related equations. This simulation leads to set forth a new concept of characteristic temperature T ₀, at which the donor population is independent of the illumination intensity G. T ₀ separates two intervals of temperature over which G either partially empties (T< T ₀) or fills (T > T ₀) the level. Also T ₀ has, in particular, an influence on the ratio n/p of free electrons and holes. The effective isothermal behaviour of n(G) shows that n(G) ∞ G ^1/2 on the lower side of the G range, and n(G) ∞ G at higher G. Variations of n(T) at constant G also display original, T ₀ dependent, characteristics. Finally, a qualitative comparison is made of the 1D model with the two 1D_ai approximate models described in I, in order to distinguish their most prominent behaviour differences.