Novel approach to the study of quantum effects in the early universe

We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function $\sigma(\eta)$ of the conformal time $\eta$, called the auxiliary field equation. At the classical level, $\sigma(\eta)$ can be expressed by means of two independent solutions of the ''master equation'' to which the perturbed Einstein equations for the gravitational waves can be reduced. At the quantum level, all the significant physical quantities can be formulated using Bogolubov transformations and the operator quadratic Hamiltonian corresponding to the classical version of a damped parametrically excited oscillator where the varying mass is replaced by the square cosmological scale factor $a^{2}(\eta)$. A quantum approach to the generation of gravitational waves is proposed on the grounds of the previous $\eta-$dependent Hamiltonian. An estimate in terms of $\sigma(\eta)$ and $a(\eta)$ of the destruction of quantum coherence due to the gravitational evolution and an exact expression for the phase of a gravitational wave corresponding to any value of $\eta$ are also obtained. We conclude by discussing a few applications to quasi-de Sitter and standard de Sitter scenarios.Comment: 20 pages, to appear on PRD. Already published background material has been either settled up in a more compact form or eliminate

Geometric phases for generalized squeezed coherent states

A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and the corresponding anholonomies deduced.Comment: 15 page

Methods for Generating Multi-scale Watershed Delineations for Indicator Development in Great Lake Coastal Ecosystems

Watersheds represent spatially explicit areas within which terrestrial stressors can be quantified and linked to measures of aquatic ecosystem condition. We delineated thousands of Great Lakes watersheds using previously proven and new watershed delineation techniques. These were used to provide summaries for a variety of anthropogenic stressors within the Great Lakes. All delineation techniques proved useful, but each had applications for which they were most appropriate. A set of watershed delineations and stressor summaries was developed for sampling site identification, providing relatively coarse strata for selecting sites along the U.S. Great Lakes coastline. Subsequent watershed delineations were used for high-resolution site characterization of specific sites and characterizing the full coastal stressor gradient. For these delineations we used three general approaches: 1) segmentation of the shoreline at points midway between adjacent streams and delineation of a watershed for each segment; 2) specific watershed delineations for sampled sites; and 3) a Great Lakes basin-wide, high-resolution approach wherein sub-basins can be agglomerated into larger basins for specific portions of the coast. The third approach is unique in that it provides a nested framework based on hierarchies of catchments with associated stressor data. This hierarchical framework was used to derive additional watershed delineations, and their associated stressor summaries, at four different scales. Providing anthropogenic stressor metrics in such a format that can quickly be summarized for the entire basin at multiple scales, or specifically for particular areas, establishes a strong foundation for quantifying and understanding stressor-response relationships in these coastal environments