Unitary transformation treatment of a single hole in an Ising antiferromagnet

The behavior of a single hole in a two-dimensional Ising antiferromagnet (t-J ^z model), is studied in the generalized Dyson-Maleev representation, where the spins are mapped on boson operators and the hole is described as a spinless fermion. The formal similarity with Fröhlich's polaron Hamiltonian suggests that thet-J ^z model can be approximately diagonalized by means of two successive unitary transformations, analogous to those used by Lee, Low, and Pines in their intermediate-coupling treatment of the polaron. Our approach yields an upper bound to the exact ground state energy, as well as the corresponding ground state eigenvector. Fork=0 our energy bound is remarkably close to the result of the self-consistent Born approximation over a wide range of the coupling parameter, which includes the range typically assumed for the high-T _c materials. The ground state eigenvector is used to calculate the spatial distribution of bosons (spin deviations) surrounding the hole. Here our results are qualitatively very similar to those obtained in previous work, showing that our ground state eigenvector accounts quite well for the small size of the “spin polaron” in thet-J ^z model.     

Pulsed photothermal laser deflection for low-level smoke and NO2 measurements in engine exhausts

Pulsed Photothermal Laser Deflection (PLD) is developed to make temporally and spatially resolved measurements of NO₂ and smoke. The rapid response PLD signal is produced when a HeNe probe beam is deflected by a thermal lens produced by a pulsed XeCl-excimer laser pumped dye laser. The fast time response (30 ns) and good spatial resolution make the PLD method a candidate for future in situ measurements in turbulent engine exhausts. The PLD signals, measured in a sample cell, exhibit a linear response for NO₂ concentrations from 3 ppm to 208 ppm and for smoke concentrations from 0.3 mg/m³ to 10 mg/m³. With a low pulse energy of 4 mJ, single-shot PLD measurements in a sample cell have accuracies of ± 14 ppm for NO₂ indicating accuracies of ±0.7 mg/m³ for smoke. With increased pulse energy and multi-shot averaging, sensitivities of ± 0.4 ppm of NO₂ or ± 20 µg/m³ of smoke are expected.     

Mosco approximation of integrands and integral functionals

It is shown that, given a lower semicontinuous convex integrandf satisfying a suitable integrability condition, there exists a sequence of Lipschitz simple integrands which Mosco converges tof and such that the sequence of conjugate integrands Mosco converges tof ^*. Moreover, this sequence can be chosen so that the sequence of associated integral functionals, respectively defined onL ¹(X) andL (X ^*), Mosco converges as well.We wish to thank Professor Erik J. Balder for interesting remarks on the first version of this work.