Spectral Analysis of Unitary Band Matrices

 This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems. These doubly infinite matrices essentially depend on an infinite sequence of phases which govern their spectral properties. We prove the spectrum is purely singular for random phases and purely absolutely continuous in case they provide the doubly infinite matrix with a periodic structure in the diagonal direction. We also study some properties of the singular spectrum of such matrices considered as infinite in one direction only. Received: 29 April 2002 / Accepted: 7 August 2002 Published online: 20 January 2003 Communicated by B. Simon     

Dilations and Mehler's kernel

An explicit formula for the second quantization of a contraction matrix on a finite dimensional Hilbert space is derived by means of dilation theory. When the dimension is one, this reduces to Mehler's formula.Supported by NSF Grant MCS-74-07313-A03     

Coherent combination of high-power, zigzag slab lasers

We demonstrate a scalable architecture for a high-power, high-brightness, solid-state laser based on coherent combinations of master oscillator power amplifier chains. A common master oscillator injects a sequence of multikilowatt Nd:YAG zigzag slab amplifiers. Adaptive optics correct the wavefront of each amplified beamlet. The beamlets are tiled side by side and actively phase locked to form a single output beam. The laser produces 19 kW with beam quality <2x diffraction limited. To the best of our knowledge, this is the brightest cw solid-state laser demonstrated to date.     

The effects of electronic polarization on water adsorption in metal-organic frameworks: H(2)O in MIL-53(Cr)

The effects of electronic polarization on the adsorption of water in the MIL-53(Cr) metal-organic framework are investigated using molecular dynamics simulations. For this purpose a fully polarizable force field for MIL-53(Cr) was developed which is compatible with the ab initio-based TTM3-F water model. The analysis of the spatial distributions of the water molecules within the MIL-53(Cr) nanopores calculated as a function of loading indicates that polarization effects play an important role in the formation of hydrogen bonds between the water molecules and the hydroxyl groups of the framework. As a result, large qualitative differences are found between the radial distribution functions calculated with non-polarizable and polarizable force fields. The present analysis suggests that polarization effects can significantly impact molecular adsorption in metal-organic frameworks under hydrated conditions.     

Preconditioned iterative methods for coupled discretizations of fluid flow problems

Computational fluid dynamics, where simulations require largecomputation times, is one of the areas of application of highperformance computing. Schemes such as the SIMPLE (semi-implicitmethod for pressure-linked equations) algorithm are often usedto solve the discrete Navier-Stokes equations. Generally theseschemes take a short time per iteration but require a largenumber of iterations. For simple geometries (or coarser grids)the overall CPU time is small. However, for finer grids or morecomplex geometries the increase in the number of iterationsmay be a drawback and the decoupling of the differential equationsinvolved implies a slow convergence of rotationally dominatedproblems that can be very time consuming for realistic applications.So we analyze here another approach, DIRECTO, that solves theequations in a coupled way. With recent advances in hardwaretechnology and software design, it became possible to solvecoupled Navier-Stokes systems, which are more robust but implyincreasing computational requirements (both in terms of memoryand CPU time). Two approaches are described here (band blockLU factorization and preconditioned GMRES) for the linear solverrequired by the DIRECTO algorithm that solves the fluid flowequations as a coupled system. Comparisons of the effectivenessof incomplete factorization preconditioners applied to the GMRES(generalized minimum residual) method are shown. Some numericalresults are presented showing that it is possible to minimizeconsiderably the CPU time of the coupled approach so that itcan be faster than the decoupled one.     

Abstract stationary theory of multichannel scattering

The abstract stationary theory of Kato and Kuroda is applied to multichannel scattering problems. It is shown that stationary wave operators exist and are asymptotically complete whenever the resolvent can be completely described in terms of primary singularities for a commuting family of channel Hamiltonians. The abstract theory is applied to prove asymptotic completeness in the three-body problem with pair potentials in L₂$\text{R}$³ for $\text{p >}\text{3}\text{2}$.