7,825 research outputs found
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
Further Evidence of a New Factor in the B Complex
The vitamin B complex is generally accepted as containing at least five distinct components for the rat; B1 (thiamin), flavin, nicotinic acid, B6, and the filtrate factor. Work by Jukes and Babcock (1) and by Oleson and co-workers (2) indicates that a distinct antiparalytic factor (very likely Reader\u27s B4 ) exists. Stocks tad (3) has reported a growth factor U for the chick. One of the authors (4) has given evidence of the existence of still another factor, the 8B factor, in the B complex. That chondroitin sulfuric acid is a growth factor for the rat has been suggested by Robinson and co-workers (5). This paper deals with further study of the SB factor and its relation to the other factors
Local dynamics in high-order harmonic generation using Bohmian trajectories
We investigate high-order harmonic generation from a Bohmian-mechanical
perspective, and find that the innermost part of the core, represented by a
single Bohmian trajectory, leads to the main contributions to the high-harmonic
spectra. Using time-frequency analysis, we associate this central Bohmian
trajectory to an ensemble of unbound classical trajectories leaving and
returning to the core, in agreement with the three step model. In the Bohmian
scenario, this physical picture builds up non-locally near the core via the
quantum mechanical phase of the wavefunction. This implies that the flow of the
wavefunction far from the core alters the central Bohmian trajectory. We also
show how this phase degrades in time for the peripheral Bohmian trajectories as
they leave the core region.Comment: 7 pages, 3 figures; the manuscript has been considerably extended and
modified with regard to the previous version
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
A causal look into the quantum Talbot effect
A well-known phenomenon in both optics and quantum mechanics is the so-called
Talbot effect. This near field interference effect arises when infinitely
periodic diffracting structures or gratings are illuminated by highly coherent
light or particle beams. Typical diffraction patterns known as quantum carpets
are then observed. Here the authors provide an insightful picture of this
nonlocal phenomenon as well as its classical limit in terms of Bohmian
mechanics, also showing the causal reasons and conditions that explain its
appearance. As an illustration, theoretical results obtained from diffraction
of thermal He atoms by both N-slit arrays and weak corrugated surfaces are
analyzed and discussed. Moreover, the authors also explain in terms of what
they call the Talbot-Beeby effect how realistic interaction potentials induce
shifts and distortions in the corresponding quantum carpets.Comment: 12 pages, 6 figure
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
per spectral element) on the variability of the {\it dust spectrum}
over 1 year, 3.3% (1 ) on the broad-band disk emission over 4 years,
and 33% (1 ) 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 HO 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 1 AU location for the emitting
material
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
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
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