Cross correlations in the longitudinal relaxation of strongly coupled spins

A generalized set of magnetization modes for quantifying cross-correlation contributions to longitudinal relaxation in strongly coupled spin systems is described in this paper. Such a set of modes (called longitudinal multiple-quantum modes) is used to unravel cross-correlation information in strongly coupled systems, where the strength of the J coupling tends to obscure such effects. The applicability of such methods is demonstrated for a small molecule which exhibits some strong coupling effects even at high magnetic field strengths. The contribution of "remote" cross correlations to the longitudinal relaxation of strongly coupled spins is detailed. Copyright 2000 Academic Press.     

Constrained fermionic system and its equivalence with the free parafermionic theory and nonlinear sigma model

We construct the parafermionic (of orderq) representation of the Kac-Moody and Virasoro algebra and compare it with a constrained fermionic system. We find that the central charge of the Virasoro algebra of the constrained fermionic system depends on the regularization scheme. Using the path integral method, we demonstrate this dependence for theq=2 case and find that it can have the same central charge as the free parafermionic theory or the non-linear sigma model depending on the regularization scheme. We point out some ambiguity in the quantization of the constrained system in Hamiltonian formulation.     

A duality theorem for continuous-time linear programming problems

Summary In dealing with dynamic economic policy models one encounters optimization problems whose objective function is an integral of a linear function of a finite number of continuous variables and whose constraints are linear integral inequalities. A set of intertemporal efficiency conditions (equilibrium conditions) yielding the optimal policy are given. By approximating the continuous problem by a set of discrete problems and appealing to a well known convergence theorem in functional analysis a continuous analog of the duality theorem is proved.

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Zusammenfassung Bei der Beschäftigung mit dynamischen Modellen der ökonomischen Politik stößt man auf Optimierungsprobleme, deren Zielfunktion ein Integral einer linearen Funktion von einer endlichen Anzahl stetiger Variablen ist und deren Beschränkungen lineare Integral-Ungleichungen sind. Eine Menge intertemporaler Effizienz-Bedingungen (Gleichgewichtsbedingungen), die zur optimalen Politik führen, sind gegeben. Durch Approximation des kontinuierlichen Problems mittels einer Menge von diskreten Problemen und Berufung auf einen wohlbekannten Konvergenzsatz aus der Funktionalanalysis wird ein stetiges Analogon des Dualitätstheorems bewiesen.

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The author is indebted to Mr.Arnold Faden for helpful suggestions and to ProfessorKarl A. Fox andGerhard Tintner for encouragement during the preparation of the paper. This research has been partially supported by a grant from the Ford Foundation to the School of Business Administration administered by the Center for Research in Management Science, University of California, Berkeley.

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Vorgel. v.:G. Tintner.     

Non-representability of cohomology classes by bi-invariant forms (gauge and Kac-Moody groups)

We give a necessary topological condition on a cohomology class of any Lie group, modelled on a Fréchet space, to be representable by a bi-invariant form on. As a corollary, we show that if for somed>0, then there exists a cohomology class in which cannot be represented by any bi-invariant form. In particular, we conclude that there are many cohomology generators, in general, in the case of gauge groups and also Kac-Moody groups which cannot be represented by bi-invariant forms, although, very often, they are representable by left invariant forms.     

A generalization of Cachazo–Douglas–Seiberg–Witten conjecture for symmetric spaces

We extend the original Cachazo–Douglas–Seiberg–Witten conjecture on the structure of the chiral ring of classical supersymmetric Yang-Mills theory to symmetric spaces.     

Unidirectional optical Bloch oscillations in asymmetric waveguide arrays

We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. It is shown that the presence of nonreciprocity in the system allows for a complete normal-mode dephasing in one of the propagation directions, resulting in a unidirectional breakdown in Bloch oscillations. A model system consisting of an array of transversely magnetized asymmetric Si/SiO2 waveguides with a magneto-optic cover layer is presented. Large index contrasts between film and cover are critical for practical realizations.     

One-neutron stripping reactions of <Superscript>11</Superscript>Be and <Superscript>19</Superscript>C on light target

We have calculated the one-neutron absorption cross-section and the longitudinal momentum distribution of the core fragment coming out from the breakup of ¹¹Be and ¹⁹C on ⁹Be target at 63 MeV/A and 88 MeV/A beam energies respectively. The reaction mechanism is treated within the framework of the eikonal approximation. The effective range of the nuclear interaction between the core and the valence neutron within the projectile has been determined by comparing the predicted stripping cross-section with the recently measured one. The effective range for ¹⁹C has been found to be smaller than that for ¹¹Be. It qualitatively indicates that ¹⁹C is slightly more halo than ¹¹Be. The smaller width, predicted as well as measured, of the LMD of ¹⁸C than ¹⁰Be also strengthens this fact. The experimental data concerning the LMD of core fragments have been well represented.      

Design,construction and characterization of the compact ultrafast terahertz free-electron laser undulator

A compact ultrafast terahertz (CUTE) free-electron laser (FEL) is being developed at the Raja Ramanna Centre for Advanced Technology (RRCAT), Indore. The undulator required for the CUTE-FEL has recently been developed. We have designed, built and characterized a variable gap, 5 cm period, 2.5 m long pure permanent magnet undulator in two identical segments. The tolerable error in the magnetic field was 1% in rms, and we have measured it to be 0.7%. The obtained rms phase shake is around 2°. To ensure that the trajectories do not have an exit error in position or angle, corrector coils have been designed. Shimming coils have been applied for both the undulator segments to reduce the amplitude of the betatron oscillations in the vertical trajectory. Details of novel corrector coils and soft iron shims are given and their performance is discussed.      

Role of Yb and Tm ions in upconversion emission of Tb under 798 and 980 nm laser excitations in Tb-Tm-Yb doped tellurite glass

Upconversion emission and energy transfer processes in singly, doubly and triply doped tellurite glasses have been studied under 798 and 980 nm laser excitations. Emissions have been observed at 482, 544, 584, 655 nm and at 477, 655, 698, 800 nm corresponding to Tb³⁺: ⁵D₄ → ⁷F₆, ⁷F₅, ⁷F₄, ⁷F_J (J = 0, 1, 2, 3) and Tm³⁺: ¹G₄ → ³H₆, ¹G₄ → ³F₄, ³F₃ → ³H₆, ³H₄ → ³H₆ transitions, respectively. Among Tm³⁺, Yb³⁺and Tb³⁺ ions only Tm³⁺ has a ground state absorption at 798 nm excitation due to ³H₄ ← ³H₆ transition. For 980 nm excitation only Yb³⁺ can absorb the incident radiation. However, for both types of excitations, emission from all the three ions Tb, Yb and Tm has been observed. Possible mechanisms are proposed as follows: under 798 nm excitation Tm³⁺ ions are excited which excite Yb³⁺ ions through energy transfer. Finally “cooperative energy transfer” from a pair of Yb³⁺ ions to Tm³⁺ and Tb³⁺ ions takes place. Under 980 nm excitation Yb³⁺ ions absorb the incident energy and excite Tm³⁺ and Tb³⁺ ions via cooperative energy transfer. Variation of emission intensity with the ion concentrations of Yb³⁺, Tm³⁺ and Tb³⁺ has been studied. The lifetime of the ¹G₄ level has also been measured.