Regge description of high energy pion pion total cross sections

We have recently presented a Regge description of pion-pion total cross sections valid above 1.4 GeV, consistent with the few existing experiments, factorization and crossing symmetry. In this note we show how it also describes a further large data sample obtained from an analysis of experiments on $\pi^\pm p\to X\Delta^{++}$ and $\pi^\pm n\to Xp$.Comment: 3 pages. To appear in the proceedings of the MESON 2004 workshop, Krakow, July 2004, to be published in Int. J. Mod. Phys.

Theoretical spectroscopy: Full quantum dynamical study of the vibrational structure of hydrated hydroxide

In many processes, the impact of nuclear quantum phenomena cannot be neglected if a physically correct simulation is aimed for [1]. This quantum description of the nuclear motion is usually obtained by mapping the system onto a grid, thus implying a discretisation of the configuration space. As a consequence, all quantities take the form of high-order tensors. Unfortunately, multidimensional representations imply an exponential scaling of data and the concomitant number of operations with system size as well as the difficulty of computing multidimensional integrals [2]. Solutions to these issues, in particular when considering the representation of the potential energy surface, exist in the form of tensor-decomposition schemes. We present the recently developed the Multigrid POTFIT (MGPF) algorithm [3] which alleviates the exponential scaling by avoiding the calculations on the full grid. Moreover, we introduceour latest improvements to the algorithm which provide numerical stability and higher accuracy through the use of non-product grids for combined modes [4]. We illustrate the power of the MGPF algorithm in conjunction with the Multiconfiguration Time-Dependent Hartree (MCTDH) method in the case of the full-dimensional (9D) study of the vibrational structure [5] and the computation of the infrared spectrum [6] of the hydrated hydroxide complex (H3O2-). [1] Fabien Gatti (Ed.) in Molecular Quantum Dynamics From Theory to Applications. Springer (2014). [2] H.-D. Meyer, F. Gatti, G. A. Worth (Eds.) Multidimensional Quantum Dynamics: MCTDH Theory and Applications, Wiley (2009). [3] D. Peláez, H.D. Meyer, The multigrid POTFIT (MGPF) method: Grid representations of potentials for quantum dynamics of large systems, J. Chem. Phys., 138, 014108 (2013). [4] D. Peláez, H.D. Meyer (in preparation) [5] D. Peláez, K. Sadri, H.-D. Meyer, Full-dimensional MCTDH/MGPF study of the ground and lowest lying vibrational states of the bihydroxide complex, Spectrochimica Acta Part A,119, 42 (2014). [6] D. Peláez, H.D. Meyer, On the infrared absorption spectrum of the hydrated hydroxide (H3O2-) cluster anion, Chem. Phys., (in press) (2016).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Schatten classes of integration operators on Dirichlet spaces

We address the question of describing the membership to Schatten-Von Neumann ideals $\mathcal{S}_ p$ of integration operators $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ acting on Dirichlet type spaces. We also study this problem for multiplication, Hankel and Toeplitz operators. In particular, we provide an extension of Luecking's result on Toeplitz operators.Comment: Accepted for publication in Journal d' Analyse Mathem\'atique, (2012