Overlapping resonances in the control of intramolecular vibrational redistribution

Coherent control of bound state processes via the interfering overlapping resonances scenario [Christopher et al., J. Chem. Phys. 123, 064313 (2006)] is developed to control intramolecular vibrational redistribution (IVR). The approach is applied to the flow of population between bonds in a model of chaotic OCS vibrational dynamics, showing the ability to significantly alter the extent and rate of IVR by varying quantum interference contributions.Comment: 10 pages, 7 figure

Malmheden's theorem revisited

In 1934 H. Malmheden discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin 23 years later, it still does not seem to be widely known. In this paper we return to Malmheden's theorem, give an alternative proof of the result that allows generalization to polyharmonic functions and, also, discuss applications of his theorem to geometric properties of harmonic measures in balls in Euclidean spaces

Two-dimensional shapes and lemniscates

A shape in the plane is an equivalence class of sufficiently smooth Jordan curves, where two curves are equivalent if one can be obtained from the other by a translation and a scaling. The fingerprint of a shape is an equivalence of orientation preserving diffeomorphisms of the unit circle, where two diffeomorphisms are equivalent if they differ by right composition with an automorphism of the unit disk. The fingerprint is obtained by composing Riemann maps onto the interior and exterior of a representative of a shape in a suitable way. In this paper, we show that there is a one-to-one correspondence between shapes defined by polynomial lemniscates of degree n and nth roots of Blaschke products of degree n. The facts that lemniscates approximate all Jordan curves in the Hausdorff metric and roots of Blaschke products approximate all orientation preserving diffeomorphisms of the circle in the C^1-norm suggest that lemniscates and roots of Blaschke products are natural objects to study in the theory of shapes and their fingerprints

Social Security, Retirement and Wealth: Theory and Implications

The effect of Social Security rules on the age people choose to retire can be critical in evaluating proposed changes to those rules. This research derives a theory of retirement that views retirement as a special type of labor supply decision. This decision is driven by wealth and substitution effects on labor supply, interacting with a fixed cost of working that makes low hours of work unattractive. The theory is tractable analytically, and therefore well-suited for analyzing proposals that affect Social Security. This research examines how retirement age varies with generosity of Social Security benefits. A ten-percent reduction in the value of benefits would lead individuals to postpone retirement by between one-tenth and one-half a year. Individuals who are relatively buffered from the change—because they are wealthier or because they are younger and therefore can more easily increase saving to offset the cut in benefits— will have smaller changes in their retirement ages. Authors’ Acknowledgements This work was supported by a grant from the Social Security Administration through the Michigan Retirement Research Center (Grant #10-P-98358-5). The opinions and conclusions are solely those of the authors and should not be considered as representing the opinions or policy of the Social Security Administration or any agency of the Federal Government. The authors gratefully acknowledge this support.

Field-free molecular orientation by THz laser pulses at high temperature

We investigate to which extend a THz laser pulse can be used to produce field-free molecular orientation at high temperature. We consider laser pulses that can be implemented with the state of the art technology and we show that the efficiency of the control scheme crucially depends on the parameters of the molecule. We analyze the temperature effects on molecular dynamics and we demonstrate that, for some molecules, a noticeable orientation can be achieved at high temperature.Comment: 13 pages, 7 figure