Action of the loop group on the self dual Yang-Mills equation

Recently Kac-Moody symmetry has played an important role in mathematical physics. Dolan and Chau, Ge and Wu discovered an infinitesimal action of the Kac-Moody Lie algebra on the space of solutions of SDYM. We have discovered an action of the loop group on the space of generalized solutions of SDYM, which exponentiates the Kac-Moody action. The group acts by adding a special type of source onto the solution. The action is a geometric construction using the twistor picture.     

Non-linear multi-plane wave solutions of self-dual Yang-Mills theory

New solutions of self-dual Yang-Mills (SDYM) equations are constructed in Minkowski space-time for the gauge groupSL(2, ). After proposing a Lorentz covariant formulation of Yang's equations, a set of Ansätze for exact non-linear multiplane wave solutions are proposed. The gauge fields are rational functions ofe ^x·ki (K _i ² =0, 1iN) for these Ansätze. At least, three families of multisoliton type solutions are derived explicitly. Their asymptotic behaviour shows that non-linear waves scatter non-trivially in Minkowski SDYM.On leave from LPTHE Université Paris VI, 4, Place Jussieu, Tour 16, ler étage, F-75230 Paris Cedex 05, France     

The linear system for self-dual gauge fields in a spacetime of signature 0

The overdetermined linear system for the self-dual Yang—Mills (SDYM) equations is examined in a flat four-dimensional space whose metric has signature 0. There are three different domains for the system, and correspondingly three (essentially) different solutions to the linear system for a given gauge field. If the gauge potential is real analytic, two of the solutions patch together to give a holomorphic function in an annular region of projective twistor space. Conversely, an arbitrary holomorphic GL(n, )-valued function in such a domain can be uniquely factored (on the real lines) to give a solution to SDYM with gauge group U(n). The set of all real analytic u(n)-valued gauge fields can thus be parametrized by the points of a certain double coset space.     

Loop Group-Valued CS and WZNW models,integrable systems,and self-dual Yang-Mills theory

Affine CS and WZNW theories with values in infinite-dimensional (loop) groups are proposed. It appears that the affine CS theory naturally introduces a spectral parameter into a CS theory. The Sinh-Gordon, KdV, and nonlinear Schrödinger equations are obtained, via Hamiltonian reductions, from the affine WZNW. It is shown that the self-dual Yang-Mills (SDYM) equation is related to the equation of motion of the affine WZNW and, thus, symmetry algebra underlying the SDYM can be identified with the affine two-loop Kac-Moody algebra of the affine WZNW.K. C. Wong Research Award Winner, address after 28 October 1992: Department of Mathematics, University of Queensland, Brisbane, Queensland 4072, Australia.     

SELF-DUAL YANG-MILLS FIELDS IN STATIC AXIALLY SYMMETRIC CASE AND RELATED TOPICS

In this article we will present an explicit geometric picture about the complete integrability of the static axially symmetric SDYM equation and the gravitational Ernst equation, interpret the correspondence between their Bäcklund transformation formulae and the transformations from one focal surface of Weingarten congruence to the integrability of the B.T.will be proved. It is shown that for the axially symmetric SDYM equation and gravitational Ernst equation the adjoint space of the group (SL(2r)) is a 3-dimensional Minkowski space, and the corresponding soliton surfaces have negative variable curvature. After introducing the generator R we can explain the B.T. as the rotation around the common tangent between two surfaces of solitons. Using Roccato eqiatopm we will confirm in this paper the integrability of B.T. amd prpve that the B.T. is strong, i. e. , the nwe and old solutions satisfy equations of motion separately. Some related topics are also discussed.     

The Hidden Symmetries and Their Algebraic Structure of the Static Axially Symmetric SDYM Fields

A new explicit transformation about the static axially symmetric self-dual Yang-Mills(SDYM) fields is presented.The theory has proved that the new transformation is a symmetric one.For the two kinds of the Lie algebraic generators of the Lie group SL (N.R)/SO(N),the corresponding transformations are given.By making use of the Yang-Baxter equality and their square brackets we have obtained the Loop and comformal algebraic structures of the symmetric transformations for the basic fields.All the results obtained in this paper can be directly generalized to the other models.     

Calculation and optimization of parameters of radiating distributed feedback structures

A simple method is suggested for calculation of reflection, radiation and transmission coefficients for the distributed feedback structure in the second diffraction order. The method is based on a slight difference between coefficients of reflectionR and radiationI of the surface wave for = (where is the light wavelength corresponding to a precise resonance for the grating length I) and those for =_l (where _l is the light wavelength corresponding to the resonance for the finite grating length). The simplicity of the method makes it possible to use it for optimization of the distributed feedback structure by a number of parameters. The technique can be used in the case of thin-film and diffused waveguides for both TE and TM modes.     

Analysis of the effects of doping and barrier design on the small-signal modulation characteristics of long-wavelength multiple quantum well lasers

This theoretical work has modelled the small signal response of InGaAsP and InGaAlAs multiple quantum well (MQW) lasers based on an ambipolar carrier transport model. The MQW parameters such as barrier bandgap, barrier width and the number of quantum wells have been optimized for high-speed modulation. The effect of the p-type doping and the strain of the InGaAs well have also been investigated.For the InGaAsP-based system, the optimization for maximum 3 dB bandwitdth shows that the optimum width is about 5 nm for 1.1 m barriers and 7 nm for 1.2 m barriers. The optimum barrier bandgap wavelength is about 1.1 m for the barrier width of 6 nm, about 1.15 m for 8 nm and 10 nm barriers. The p-doped MQW exhibits a higher modulation bandwidth because of its high differential gain and improved carrier distribution among the MQWs. The compressively strained InGaAs quantum well system has the potential for a higher modulation bandwidth. For the InGaAlAs-based system, the optimization for maximum 3 dB bandwidth shows that the optimum width is about 4 nm for a barrier wavelength of 1.10 m, and 6 nm for 1.2 m. The optimum barrier bandgap wavelength is about 1.1 m for a barrier width of 4 nm, and about 1.2 m for 6, 8 and 10 nm.     

Random shearing direction models for isotropic turbulent diffusion

Recently, a rigorous renormalization theory for various scalar statistics has been developed for special modes of random advection diffusion involving random shear layer velocity fields with long-range spatiotemporal correlations. New random shearing direction models for isotropic turbulent diffusion are introduced here. In these models the velocity field has the spatial second-order statistics of an arbitrary prescribed stationary incompressible isotropic random field including long-range spatial correlations with infrared divergence, but the temporal correlations have finite range. The explicit theory of renormalization for the mean and second-order statistics is developed here. With the spectral parameter, for –<<4 and measuring the strength of the infrared divergence of the spatial spectrum, the scalar mean statistics rigorously exhibit a phase transition from mean-field behavior for <2 to anomalous behavior for with 2<<4 as conjectured earlier by Avellaneda and the author. The universal inertial range renormalization for the second-order scalar statistics exhibits a phase transition from a covariance with a Gaussian functional form for with <2 to an explicit family with a non-Gaussian covariance for with 2<<4. These non-Gaussian distributions have tails that are broader than Gaussian as varies with 2<<4 and behave for large values like exp(–C _c |x|^4–), withC _c an explicit constant. Also, here the attractive general principle is formulated and proved that every steady, stationary, zero-mean, isotropic, incompressible Gaussian random velocity field is well approximated by a suitable superposition of random shear layers.     

Stability and structure of Newtonian gravitars

The solution r² for a scalar field (gravitational constant), which is asymptotically exact for supercompact configurations and which Saakyan and Mnatsakanyan obtained from the numerical solution of the hydrostatics equations in the Newtonian approximation of the Jordan-Brans-Dicke theory, is used to study the gravitational stability of such configurations. We have found the stability condition 2/3 for polytropic configurations ( is the polytropic exponent) instead of 4/3, which is known for configurations of low compactness. Analytic solutions of the equations of internal structure are found for configurations which are intermediate with respect to stability (=2/3) and for some other important series of configurations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 98–102, July, 1982.In conclusion, the present author expresses his indebtedness and gratitude to V. N. Ponomarev, for assistance in executing the work.     

Photo-induced birefringence in semiconductors compared with optical fibers

We analyze the photon-induced birefringence in semiconductors based on pump-probe setups, within the semiconductor Bloch equations formalism and the Luttinger-Kohn model for the band structure. When the pump and probe pulses are well separated in time, the anisotropic momentum space filling of the photo-excited electrons is the only mechanism causing the induced birefringence. The birefringence ratio is then for pump and probe having perpendicular vs. parallel linear polarizations. This ratio is for opposite vs. identical circular polarization. When the pump and probe pulses overlap in time, these birefringence ratios become for linear polarizations and in case of circular polarizations. These predictions differ markedly from those for optical fibers.     

Segregation of Components as a Result of High‐Power Laser Irradiation of Heterogeneous Condensed Media

The effects of periodic segregation of components in metastable (supercooled or supersaturated) binary alloys in the course of kinetic phase transformations as a result of laser irradiation of heterogeneous systems were studied analytically. Nonlinear processes of temporal and spatial selforganization of concentrationrelated structures were simulated using (i) a selfconsistent system of timedependent twodimensional equations for the distribution function for the sizes and spatial coordinates of the newphase particles and (ii) balance equations for the temperature and concentration of dissolved components; the latter equations account for nonlinearity of the particlesource function, sinks, for dependences of the phasetransition temperature on the surface curvature of particles and on the concentration of components, and for diffusive motion of particles in space. The domain of existence for the instabilities under consideration and the characteristics of the formed crystallizationrelated periodic structures are determined. It is established that nanoclusters formed during supersaturation of crystallizing material may play an important role in generation of selfoscillatory crystallization modes. Hydrodynamic aspects of liquidphase concentrationrelated stratification in heterogeneous systems based on immiscible components are considered.     

A model calculation for vibrational propagation in a chain of nonlinear oscillators

We analyze a chain of nonlinear oscillators and calculate transport quantities relevant to the propagation of vibrational excitations in the chain. We obtain explicit expressions for oscillator displacements as well as for the mean-square-displacements of the vibrational excitation for several different initial conditions including a localized and a grating initial condition, and study with their help the effects of nonlinearity on vibrational propagation.     

Coupled Cluster Method Calculations of Quantum Magnets with Spins of General Spin Quantum Number

We present a new high-order coupled cluster method (CCM) formalism for the ground states of lattice quantum spin systems for general spin quantum number, s. This new general-s formalism is found to be highly suitable for a computational implementation, and the technical details of this implementation are given. To illustrate our new formalism we perform high-order CCM calculations for the one-dimensional spin-half and spin-one antiferromagnetic XXZ models and for the one-dimensional spin-half/spin-one ferrimagnetic XXZ model. The results for the ground-state properties of the isotropic points of these systems are seen to be in excellent quantitative agreement with exact results for the special case of the spin-half antiferromagnet and results of density matrix renormalization group (DMRG) calculations for the other systems. Extrapolated CCM results for the sublattice magnetization of the spin-half antiferromagnet closely follow the exact Bethe Ansatz solution, which contains an infinite-order phase transition at =1. By contrast, extrapolated CCM results for the sublattice magnetization of the spin-one antiferromagnet using this same scheme are seen to go to zero at 1.2, which is in excellent agreement with the value for the onset of the Haldane phase for this model. Results for sublattice magnetizations of the ferrimagnet for both the spin-half and spin-one spins are non-zero and finite across a wide range of , up to and including the Heisenberg point at =1.     

First passage time problems in time-dependent fields

This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency * for which the mean residence time on the line segment is a minimum. It is shown that for a random walk on a line segment of lengthL the mean residence time goes likeL ² for largeL when *, but when =* the dependence is proportional toL. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation.     

Infinite hierarchy of exponents in a two-component random resistor network

We have studied the voltage distribution for a two-component random mixture of conductances _a and _b. A scaling theory is developed for the moments of the distribution, which predicts, for small values ofh=_a/_b, an infinite number of crossover exponents, one for each moment, for Euclidean dimensiond >2, and only one crossover exponent ford=2. Monte Carlo results on the square lattice confirm this prediction.     

Light absorption in laser-heated cavities

The absorption of laser light in 0.25–1 mm diameter gold cavities, irradiated for the purpose of generating high-temperature blackbody radiation with intense laser radiation of either =0.44 m or =1.3 m wavelength, was investigated. For =0.44 m radiation the absorption exceeded 0.9 for all conditions, but dropped to only 0.3 for the smallest cavities irradiated at =1.3 m. Entrance hole and cavity filling with plasma seems important for the understanding of the observations.     

Theoretical calculation of the isoelectronic line ratio of Li-like Ti and Cr under different mixture ratios

With the consideration of coronal conditions, a simplified model and the steady-state rate-equation are used to calculate the isoelectronic line ratio for transition in Li-like Ti and Cr from the electron temperature 400 to . The relation between the isoelectronic line ratio and the electron temperature are provided under different mixture ratios of Ti and Cr. Then, the mixture ratio from 2:1 to 3:1 between Ti and Cr are obtained that are suitable for the electron temperature diagnostic by using isoelectronic line ratio of Li-like Ti and Cr. The relative abundance of two close ionization stages, which is from bare nucleus to Be-like ionization stage, are given and show that the He-, Li- and Be-like are the principal ionization stages from 400 to for Ti and from 500 to for Cr. The Li-like charge state will reach the maximum distribution approximately from 400 to for Ti and from 547 to for Cr. The paper also shows that the dielectronic recombination and spontaneous radiative recombination rates only have small effects on the isoelectronic line ratio in the electron temperature 400-.