Using mixed data in the inverse scattering problem

Consider the fixed-$\ell$ inverse scattering problem. We show that the zeros of the regular solution of the Schr\"odinger equation, $r_{n}(E)$, which are monotonic functions of the energy, determine a unique potential when the domain of the energy is such that the $r_{n}(E)$ range from zero to infinity. This suggests that the use of the mixed data of phase-shifts $\{\delta(\ell_0,k), k \geq k_0 \} \cup \{\delta(\ell,k_0), \ell \geq \ell_0 \}$, for which the zeros of the regular solution are monotonic in both domains, and range from zero to infinity, offers the possibility of determining the potential in a unique way.Comment: 9 pages, 2 figures. Talk given at the Conference of Inverse Quantum Scattering Theory, Hungary, August 200

Scaling limits of integrable quantum field theories

Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is shown that massless scaling limit theories exist, and decompose into (twisted) tensor products of chiral, translation-dilation covariant field theories. On the subspace which is generated from the vacuum by the observables localized in finite light ray intervals, this symmetry can be extended to the M\"obius group. The structure of the interval-localized algebras in the chiral models is discussed in two explicit examples.Comment: Revised version: erased typos, improved formulations, and corrections of Lemma 4.8/Prop. 4.9. As published in RMP. 43 pages, 1 figur

Nonuniversal correlations in multiple scattering

We show that intensity of a wave created by a source embedded inside a three-dimensional disordered medium exhibits a non-universal space-time correlation which depends explicitly on the short-distance properties of disorder, source size, and dynamics of disorder in the immediate neighborhood of the source. This correlation has an infinite spatial range and is long-ranged in time. We suggest that a technique of "diffuse microscopy" might be developed employing spatially-selective sensitivity of the considered correlation to the disorder properties.Comment: 15 pages, 3 postscript figures, accepted to Phys. Rev.

Potencial da espectroscopia de fluorescência induzida por laser para separar variedades de laranja geneticamente parecidas.

Entrada padronizada: VILLAS-BOAS, P. R