7,824 research outputs found
Unified derivation of Bohmian methods and the incorporation of interference effects
We present a unified derivation of Bohmian methods that serves as a common
starting point for the derivative propagation method (DPM), Bohmian mechanics
with complex action (BOMCA) and the zero-velocity complex action method
(ZEVCA). The unified derivation begins with the ansatz
where the action, , is taken to be complex and
the quantum force is obtained by writing a hierarchy of equations of motion for
the phase partial derivatives. We demonstrate how different choices of the
trajectory velocity field yield different formulations such as DPM, BOMCA and
ZEVCA. The new derivation is used for two purposes. First, it serves as a
common basis for comparing the role of the quantum force in the DPM and BOMCA
formulations. Second, we use the new derivation to show that superposing the
contributions of real, crossing trajectories yields a nodal pattern essentially
identical to that of the exact quantum wavefunction. The latter result suggests
a promising new approach to deal with the challenging problem of nodes in
Bohmian mechanics
Emerging Trends in Child Protective Work During the Progressive Era 1909-1929: Local Experience in a National Context
This historical analysis seeks to inform current
debate in child welfare practice through analysis of the
development of child protection work in the United States
during the Progressive Era. Analysis of case records and
social work debate suggests a shift occurred in the
intervention strategy used by social workers in their
approach to child protective work. Social workers shifted
from a social control model to a casework intervention
strategy in protective work. Case records from the
Children\u27s Protective Society of Hennepin County in the
1920s depict a combination of both intervention strategies
being utilized simultaneously
Acetylene terminated matrix resins
The synthesis of resins with terminal acetylene groups has provided a promising technology to yield high performance structural materials. Because these resins cure through an addition reaction, no volatile by-products are produced during the processing. The cured products have high thermal stability and good properties retention after exposure to humidity. Resins with a wide variety of different chemical structures between the terminal acetylene groups are synthesized and their mechanical properties studied. The ability of the acetylene cured polymers to give good mechanical properties is demonstrated by the resins with quinoxaline structures. Processibility of these resins can be manipulated by varying the chain length between the acetylene groups or by blending in different amounts of reactive deluents. Processing conditions similar to the state-of-the-art epoxy can be attained by using backbone structures like ether-sulfone or bis-phenol-A. The wide range of mechanical properties and processing conditions attainable by this class of resins should allow them to be used in a wide variety of applications
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
Semiclassical approximation with zero velocity trajectories
We present a new semiclassical method that yields an approximation to the
quantum mechanical wavefunction at a fixed, predetermined position. In the
approach, a hierarchy of ODEs are solved along a trajectory with zero velocity.
The new approximation is local, both literally and from a quantum mechanical
point of view, in the sense that neighboring trajectories do not communicate
with each other. The approach is readily extended to imaginary time propagation
and is particularly useful for the calculation of quantities where only local
information is required. We present two applications: the calculation of
tunneling probabilities and the calculation of low energy eigenvalues. In both
applications we obtain excellent agrement with the exact quantum mechanics,
with a single trajectory propagation.Comment: 16 pages, 7 figure
Complex trajectory method in time-dependent WKB
We present a significant improvement to a time-dependent WKB (TDWKB)
formulation developed by Boiron and Lombardi [JCP {\bf108}, 3431 (1998)] in
which the TDWKB equations are solved along classical trajectories that
propagate in the complex plane. Boiron and Lombardi showed that the method
gives very good agreement with the exact quantum mechanical result as long as
the wavefunction does not exhibit interference effects such as oscillations and
nodes. In this paper we show that this limitation can be overcome by
superposing the contributions of crossing trajectories. We also demonstrate
that the approximation improves when incorporating higher order terms in the
expansion. These improvements could make the TDWKB formulation a competitive
alternative to current time-dependent semiclassical methods
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