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

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

Spin-dependent Bohm trajectories associated with an electronic transition in hydrogen

The Bohm causal theory of quantum mechanics with spin-dependence is used to determine electron trajectories when a hydrogen atom is subjected to (semi-classical) radiation. The transition between the 1s ground state and the 2p0 state is examined. It is found that transitions can be identified along Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of revolution in R^3. The energy along the trajectories is also discussed in relation to the hydrogen energy eigenvalues.Comment: 18 pages, 8 figure

Bose-Einstein Condensation at a Helium Surface

Path Integral Monte Carlo was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at $T=0.77 K$, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9 before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. Finally, a surface dispersion relation was calculated from imaginary-time density-density correlations.Comment: 8 pages, 5 figure

Radiation effects on silicon solar cells Final report, Dec. 1, 1961 - Dec. 31, 1962

Displacement defects in silicon solar cells by high energy electron irradiation using electron spin resonance, galvanometric, excess carrier lifetime, and infrared absorption measurement

Multi-Epoch Observations of HD69830: High Resolution Spectroscopy and Limits to Variability

The main-sequence solar-type star HD69830 has an unusually large amount of dusty debris orbiting close to three planets found via the radial velocity technique. In order to explore the dynamical interaction between the dust and planets, we have performed multi-epoch photometry and spectroscopy of the system over several orbits of the outer dust. We find no evidence for changes in either the dust amount or its composition, with upper limits of 5-7% (1 $\sigma$ per spectral element) on the variability of the {\it dust spectrum} over 1 year, 3.3% (1 $\sigma$) on the broad-band disk emission over 4 years, and 33% (1 $\sigma$) on the broad-band disk emission over 24 years. Detailed modeling of the spectrum of the emitting dust indicates that the dust is located outside of the orbits of the three planets and has a composition similar to main-belt, C-type asteroids asteroids in our solar system. Additionally, we find no evidence for a wide variety of gas species associated with the dust. Our new higher SNR spectra do not confirm our previously claimed detection of H$_2$O ice leading to a firm conclusion that the debris can be associated with the break-up of one or more C-type asteroids formed in the dry, inner regions of the protoplanetary disk of the HD69830 system. The modeling of the spectral energy distribution and high spatial resolution observations in the mid-infrared are consistent with a $\sim$ 1 AU location for the emitting material

Monte Carlo Generation of Bohmian Trajectories

We report on a Monte Carlo method that generates one-dimensional trajectories for Bohm's formulation of quantum mechanics that doesn't involve differentiation or integration of any equations of motion. At each time, t=n\delta t (n=1,2,3,...), N particle positions are randomly sampled from the quantum probability density. Trajectories are built from the sorted N sampled positions at each time. These trajectories become the exact Bohm solutions in the limits N->\infty and \delta t -> 0. Higher dimensional problems can be solved by this method for separable wave functions. Several examples are given, including the two-slit experiment.Comment: 10 pages, 6 figure

Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials

In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step, square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a future publication.Comment: 18 pages, 8 figure