Quantum Hamilton--Jacobi Approach to Two Dimensional Singular Oscillator

We obtain the solutions of two-dimensional singular oscillator which is known as the quantum Calogero-Sutherland model both in cartesian and parabolic coordinates within the framework of quantum Hamilton Jacobi formalism. Solvability conditions and eigenfunctions are obtained by using the singularity structures of quantum momentum functions under some conditions. New potentials are generated by using the first two states of singular oscillator for parabolic coordinates.     

Applications of Lie Symmetries to Higher Dimensional Gravitating Fluids

We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein’s equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie point symmetries of the fundamental field equation, we obtain either an implicit solution or we can reduce the governing equations to a Riccati equation. We show that known solutions of the Einstein equations can produce infinite families of new solutions. Earlier results in four dimensions are shown to be special cases of our generalised results.     

三维变角反射计

本文介绍了三维变角反射计的结构.检验了球形照明球的亮度均匀性、测量系统的线性性、单色仪的波长准确度和杂散辐射等参数.测定了漫射陶瓷板和海伦(Halon)粉末压制板的反射亮度分布曲线.讨论了变角反射计在色度学和光谱光度学中的重要应用.     

Exact Dimensional Reduction of Linear Dynamics: Application to Confined Diffusion

In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the “classical” Fick-Jacobs approximate reduction to an exact subdynamics.     

Dimensional crossover in quantum networks: from macroscopic to mesoscopic physics

We report on magnetoconductance measurements of metallic networks of various sizes ranging from 10 to 10(6) plaquettes, with an anisotropic aspect ratio. Both Altshuler-Aronov-Spivak h/2e periodic oscillations and Aharonov-Bohm h/e periodic oscillations are observed for all networks. For large samples, the amplitude of both oscillations results from the incoherent superposition of contributions of phase coherent regions. When the transverse size becomes smaller than the phase coherent length Lphi, one enters a new regime which is phase coherent (mesoscopic) along one direction and macroscopic along the other, leading to a new size dependence of the quantum oscillations.     

One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations

We consider u(x,t) a solution of u _t =Δu+|u| ^{p − 1} u that blows up at time T, where u:ℝ ^N ×[0, T)→ℝ, p>1, (N−2)p<N+2 and either u(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, as T−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous and N−1 dimensional, we escape logarithmic scales of the variable T−t and give a sharper expansion of the solution with the much smaller error term (T−t)^{1, 1/2−η} for any η>0. In particular, if in addition p>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it is C ^{1, 1/2−η} for any η>0. Received: 20 June 2001 / Accepted: 6 October 2001     

Dimensional reduction of symmetries

It has been shown that ordinary (d−2)-dimensional quantum field theories are equivalent to corresponding quantum field theories defined on a (d+2)-dimensional superspace with two anticommuting variables. This dimensional reduction is a consequence of superrotation invariance in the superspace. In this letter we study general conformal transformations in the superspace and the properties of field theories which are invariant under such transformations. We show that the symmetries are dimensionally reduced.     

Dimensional implications of dynamical data on manifolds to empirical KL analysis

We explore the approximation of attracting manifolds of complex systems using dimension reducing methods. Complex systems having high-dimensional dynamics typically are initially analyzed by exploring techniques to reduce the dimension. Linear techniques, such as Galerkin projection methods, and nonlinear techniques, such as center manifold reduction are just some of the examples used to approximate the manifolds on which the attractors lie. In general, if the manifold is not highly curved, then both linear and nonlinear methods approximate the surface well. However, if the manifold curvature changes significantly with respect to parametric variations, then linear techniques may fail to give an accurate model of the manifold. This may not be a surprise in itself, but it is a fact so often overlooked or misunderstood when utilizing the popular KL method, that we offer this explicit study of the effects and consequences. Here we show that certain dimensions defined by linear methods are highly sensitive when modeled in situations where the attracting manifolds have large parametric curvature. Specifically, we show how manifold curvature mediates the dimension when using a linear basis set as a model. We punctuate our results with the definition of what we call, a “curvature induced parameter,” $d_{CI}$. Both finite- and infinite-dimensional models are used to illustrate the theory.     

Dimensional regularization and supersymmetry

A detailed numerical integration of the Oppenheimer-Volkoff equations for isothermal partially degenerate neutral lepton configurations shows that the mass distribution of the dark halo around the giant elliptical galaxy M87, as revealed by X-ray observations, can be very naturally accounted for, in detail, by an atmosphere of (10–50 eV) neutrinos.     

Dimensional renormalization and factorization

The problem of formulating a high-energy factorization explicitly in terms of dimensionally renormalized operators and coefficient functions is analyzed in the context of deep-inelastic scattering in renormalizable scalar theories. The coefficient functions that emerge are found to be the finite parts of dimensionally continued on-shell amplitudes, and are readily amenable to explicit computation. As a byproduct, an explicit forest formula emerges for the mass-singularity poles of on-shell amplitudes in renormalizable theories. The extension to gauge theories is briefly discussed at the leading twist level. The method is compared to the alternative approach to factorization whereby a finite hard part is defined by factorizing off mass-singularities.     

Dimensional regularization and supersymmetry

We examine in detail the techniques of supersymmetric dimensional regularization. A peculiar complementarity is found to be inherent in the regularization: its manifestly supersymmetric version is contradictory, while the removal of inconsistencies costs a lossof supersymmetry in higher orders. We analyse this phenomenon at the level of Feynman diagrams and discover an explicit example of supersymmetry breakdown in the three-loop approximation. In the light of this result, we reconsider the status of dimensional regularization in globally supersymmetric gauge theories.     

Dimensional regularisation and instantons

Dimensional regularisation is applied to the calculation of the quantum corrections to the instanton tunnelling amplitude in an SU(2) gauge theory. The principal feature is the introduction of an n-dimensional field configuration (a “quasi-instanton”), which generalises the O(5) invariance of the instanton and allows a coordinatisation of the function space of fields in its neighbourhood. This enables the functional integral measure to be factorised, with integrations over the translation and dilatation degrees of freedom being extracted. It is shown that a conformally invariant definition of orthogonality must be used in relation to the zero-mode eigenfunctions of the small oscillations expansion, irrespective of regularisation. An O(n + 1) covariant formalism is employed. An unconventional choice of gauge fixing term, which is not a perfect square, is made and is shown to allow the important freedom of calculating in a gauge specified by an arbitrary parameter α.     

Dimensional Power Counting in Nuclei

Weinberg's dimensional power counting for nuclei is reprised in this primer. The role of QCD and chiral symmetry in constructing effective Lagrangians is discussed. The two-scale hypothesis of Manohar and Georgi is combined with power counting in amplitudes to shed light on the scales of nuclear kinetic and potential energies, the size of strong-interaction coupling constants, the size of meson-exchange currents, and the relative sizes of many-nucleon forces. Numerous examples are worked out and compared to conventional nuclear models. Received July 12, 1996; revised November 17, 1996; accepted for publication February 10, 1997     

Dimensional regularization in four dimensions

A new gauge invariant ultraviolet regularization proposed recently is discussed for Abelian gauge theories. This cut-off scheme resembles closely the canonical dimensional regularization (CDR), but it is formulated strictly in four dimensions. In a sense, it may be conceived as a continuous superposition of Pauli-Villars cut-offs. Although it differs from the CDR for a general graph, for some closed fermion loops the two schemes coincide. The new cut-off procedure is also well-suited for practical calculations of Feynman diagrams in the -parametric representation; in this respect it preserves the merits of CDR. Such a dimensional regularization in four dimensions obviously does not suffer from the conceptual problems connected with the definition of the ₅ matrix, which plague conventional DR schemes. Nevertheless, some spurious anomalies in the closed fermion loops do occur, similarly to the Pauli-Villars scheme.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.