Quantum Mechanics with Trajectories: Quantum Trajectories and Adaptive Grids

Although the foundations of the hydrodynamical formulation of quantum mechanics were laid over 50 years ago, it has only been within the past few years that viable computational implementations have been developed. One approach to solving the hydrodynamic equations uses quantum trajectories as the computational tool. The trajectory equations of motion are described and methods for implementation are discussed, including fitting of the fields to gaussian clusters.Comment: Prepared for CiSE, Computing in Science and Engineering IEEE/AIP special issue on computational chemistr

BACTERIOLOGICAL STANDARDS AND FOOD QUALITY/SAFETY

Food Consumption/Nutrition/Food Safety,

Hydrodynamic View of Wave-Packet Interference: Quantum Caves

Wave-packet interference is investigated within the complex quantum Hamilton-Jacobi formalism using a hydrodynamic description. Quantum interference leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display counterclockwise helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. The string of alternating stagnation and vortical tubes is sufficient to generate divergent trajectories. Moreover, the average wrapping time for trajectories and the rotational rate of the nodal line in the complex plane can be used to define the lifetime for interference features.Comment: 4 pages, 3 figures (major revisions with respect to the previous version have been carried out

Marine-Nonmarine Relationships in the Cenozoic Section of California

Highly fossiliferous marine sediments of Cenozoic age are widely distributed in the coastal parts of central and southern California, as well as in the Sacramento-San Joaquin Valley region farther inland. Even more widespread are nonmarine, chiefly terrestrial, sequences of Cenozoic strata, many of which contain vertebrate faunas characterized by a dominance of mammalian forms. These strata are most abundant in the Mojave Desert region and in the interior parts of areas that lie nearer the coast. Marine and nonmarine strata are in juxtaposition or interfinger with one another at many places, especially in the southern Coast Ranges and the San Joaquin basin to the east, in the Transverse Ranges and adjacent basins, and in several parts of the Peninsular Range region and the Coachella-Imperial Valley to the east. These occurrences of closely related marine and nonmarine deposits permit critical comparisons between the Pacific Coast mammalian (terrestrial) and invertebrate (marine) chronologies, and it is with these comparisons-examined in the light of known stratigraphic relations-that this paper is primarily concerned. The writers have drawn freely upon the published record for geologic and paleontologic data. In addition, Durham has reviewed many of the invertebrate faunas and has checked the field relations of marine strata in parts of the Ventura and Soledad basins, the Tejon Hills, and the Cammatta Ranch; Jahns has studied new vertebrate material from the Soledad basin and has mapped this area and critical areas in the vicinity of San Diego, in the Ventura basin, and in the Caliente Range; and Savage has made a detailed appraisal of the vertebrate assemblages, and has mapped critical areas in the Tejon Hills. The areas and localities that have been most carefully scrutinized are shown in figure 1. The manuscript was reviewed in detail by G. Edward Lewis of the U. S. Geological Survey, who made numerous comments and suggestions that resulted in considerable improvement. It should be noted that his views are not wholly compatible with some of those expressed in this paper, and that his critical appraisal thus was particularly helpful

Summary of DSN (Deep Space Network) reimbursable launch support

The Deep Space Network is providing ground support to space agencies of foreign governments as well as to NASA and other agencies of the Federal government which are involved in space activities. DSN funding for support of missions other than NASA are on either a cooperative or a reimbursable basis. Cooperative funding and support are accomplished in the same manner as NASA sponsored missions. Reimbursable launch funding and support methods are described

Interference in Bohmian Mechanics with Complex Action

In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex [JCP {125}, 231103 (2006)]. In the alternative formulation there is a significant reduction in the magnitude of the quantum force as compared with the conventional Bohmian formulation, at the price of propagating complex trajectories. In this paper we show that Bohmian mechanics with complex action is able to overcome the main computational limitation of conventional Bohmian methods -- the propagation of wavefunctions once nodes set in. In the vicinity of nodes, the quantum force in conventional Bohmian formulations exhibits rapid oscillations that pose severe difficulties for existing numerical schemes. We show that within complex Bohmian mechanics, multiple complex initial conditions can lead to the same real final position, allowing for the description of nodes as a sum of the contribution from two or more crossing trajectories. The idea is illustrated on the reflection amplitude from a one-dimensional Eckart barrier. We believe that trajectory crossing, although in contradiction to the conventional Bohmian trajectory interpretation, provides an important new tool for dealing with the nodal problem in Bohmian methods