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

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

Scattered-wave-packet formalism with applications to barrier scattering and quantum transistors

The scattered wave formalism developed for a quantum subsystem interacting with reservoirs through open boundaries is applied to one- or two-dimensional barrier scattering and quantum transistors. The total wave function is divided into incident and scattered components. Markovian outgoing wave boundary conditions are imposed on the scattered or total wave function by either the ratio or polynomial methods. For barrier scattering problems, accurate time-dependent transmission probabilities are obtained through the integration of the modified time-dependent Schrodinger equations for the scattered wave function. For quantum transistors, the time-dependent transport is studied for a quantum wave packet propagating through the conduction channel of a field effect transistor. This study shows that the scattered wave formalism significantly reduces computational effort relative to other open boundary methods and demonstrates wide applications to quantum dynamical processes.Robert Welch Foundation F-0362Chemical Engineerin

Growth Response of Kenhy Fescue to Nitrogen Fertilizer

Kenhy fescue is a new, improved variety of tall fescue which has recently been released by the University of Kentucky Agricultural Experiment Station and the U.S.D.A. Agricultural Research Service (see University of Kentucky publication AGR-60, Kenhy A New Tall Fescue Variety ). Seed of this variety should become available to farmers in limited quantities in the summer 1977. The purpose of this report is to provide information on how this newly developed fescue variety produces as affected by time and rate of nitrogen application

Quantum interference within the complex quantum Hamilton-Jacobi formalism

Quantum interference is investigated within the complex quantum Hamilton-Jacobi formalism. As shown in a previous work [Phys. Rev. Lett. 102, 250401 (2009)], complex quantum trajectories display helical wrapping around stagnation tubes and hyperbolic deflection near vortical tubes, these structures being prominent features of quantum caves in space-time Argand plots. Here, we further analyze the divergence and vorticity of the quantum momentum function along streamlines near poles, showing the intricacy of the complex dynamics. Nevertheless, despite this behavior, we show that the appearance of the well-known interference features (on the real axis) can be easily understood in terms of the rotation of the nodal line in the complex plane. This offers a unified description of interference as well as an elegant and practical method to compute the lifetime for interference features, defined in terms of the average wrapping time, i.e., considering such features as a resonant process.Comment: revised version, 13 pages, 11 figures, 1 tabl

Morphological and genetic analyses in the Melanoplus packardii group (Orthoptera: Acrididae)

Melanoplus packardii Scudder was described in 1897. Three additional closely-related species were later described and their status as species has been questioned on numerous occasions. We examined morphology from specimens collected in Nebraska which fit descriptions of three of the four forms and specimens that appeared to be hybrids. We found distinct morphological characters suggesting species status for M. foedus and M. packardii, but not for M. foedus fluviatilis. Examination of aedeagi of these three forms suggests that M. foedus and M. packardii are each distinct, but that the aedeagi of M. f. fluviatilis and M. f. foedus cannot be distinguished. Molecular analyses of the three groups did not produce clear separations and suggest gene exchange between these three forms may be ongoing. Together, these data suggest that M. foedus and M. packardii should be recognized as sibling species, but M. foedus fluviatilis is best considered a form of M. foedus, typically found in low lying areas

Morphological and genetic analyses in the Melanoplus packardii group (Orthoptera: Acrididae)

Melanoplus packardii Scudder was described in 1897. Three additional closely-related species were later described and their status as species has been questioned on numerous occasions. We examined morphology from specimens collected in Nebraska which fit descriptions of three of the four forms and specimens that appeared to be hybrids. We found distinct morphological characters suggesting species status for M. foedus and M. packardii, but not for M. foedus fluviatilis. Examination of aedeagi of these three forms suggests that M. foedus and M. packardii are each distinct, but that the aedeagi of M. f. fluviatilis and M. f. foedus cannot be distinguished. Molecular analyses of the three groups did not produce clear separations and suggest gene exchange between these three forms may be ongoing. Together, these data suggest that M. foedus and M. packardii should be recognized as sibling species, but M. foedus fluviatilis is best considered a form of M. foedus, typically found in low lying areas