28 research outputs found
Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
We introduce a pedagogical discussion on Bohmian mechanics and its physical
implications in connection with the important role played by the quantum phase
in the dynamics of quantum processes. In particular, we focus on phenomena such
as quantum coherence, diffraction, and interference, due to their historical
relevance in the development of the quantum theory and their key role in a
myriad of fundamental and applied problems of current interest.Comment: 10 pages, 5 figure
Interplay of causticity and vorticality within the complex quantum Hamilton-Jacobi formalism
Interference dynamics is analyzed in the light of the complex quantum
Hamilton-Jacobi formalism, using as a working model the collision of two
Gaussian wave packets. Though simple, this model nicely shows that interference
in quantum scattering processes gives rise to rich dynamics and trajectory
topologies in the complex plane, both ruled by two types of singularities:
caustics and vortices, where the former are associated with the regime of free
wave-packet propagation, and the latter with the collision (interference)
process. Furthermore, an unambiguous picture connecting the complex and real
frameworks is also provided and discussed.Comment: 12 pages, 3 figure
A trajectory-based understanding of quantum interference
Interference is one of the most fundamental features which characterizes
quantum systems. Here we provide an exhaustive analysis of the interfere
dynamics associated with wave-packet superpositions from both the standard
quantum-mechanical perspective and the Bohmian one.
From this analysis, clear and insightful pictures of the physics involved in
this kind of processes are obtained, which are of general validity (i.e.,
regardless of the type of wave packets considered) in the understanding of more
complex cases where interference is crucial (e.g., scattering problems, slit
diffraction, quantum control scenarios or, even, multipartite interactions). In
particular, we show how problems involving wave-packet interference can be
mapped onto problems of wave packets scattered off potential barriers.Comment: 27 pages, 12 figures (shortened version
Adsorbate surface diffusion: The role of incoherent tunneling in light particle motion
The role of incoherent tunneling in the diffusion of light atoms on surfaces
is investigated. With this purpose, a Chudley-Elliot master equation
constrained to nearest neighbors is considered within the Grabert-Weiss
approach to quantum diffusion in periodic lattices. This model is applied to
recent measurements of atomic H and D on Pt(111), rendering friction
coefficients that are in the range of those available in the literature for
other species of adsorbates. A simple extension of the model has also been
considered to evaluate the relationship between coverage and tunneling, and
therefore the feasibility of the approach. An increase of the tunneling rate
has been observed as the surface coverage decreases.Comment: 7 pages, 2 figures; important reorganization of the work (including
title changes
Phonon lineshapes in atom-surface scattering
Phonon lineshapes in atom-surface scattering are obtained from a simple
stochastic model based on the so-called Caldeira-Leggett Hamiltonian. In this
single-bath model, the excited phonon resulting from a creation or annihilation
event is coupled to a thermal bath consisting of an infinite number of harmonic
oscillators, namely the bath phonons. The diagonalization of the corresponding
Hamiltonian leads to a renormalization of the phonon frequencies in terms of
the phonon friction or damping coefficient. Moreover, when there are adsorbates
on the surface, this single-bath model can be extended to a two-bath model
accounting for the effect induced by the adsorbates on the phonon lineshapes as
well as their corresponding lineshapes.Comment: 14 pages, 2 figure
Understanding interference experiments with polarized light through photon trajectories
Bohmian mechanics allows to visualize and understand the quantum-mechanical
behavior of massive particles in terms of trajectories. As shown by
Bialynicki-Birula, Electromagnetism also admits a hydrodynamical formulation
when the existence of a wave function for photons (properly defined) is
assumed. This formulation thus provides an alternative interpretation of
optical phenomena in terms of photon trajectories, whose flow yields a
pictorial view of the evolution of the electromagnetic energy density in
configuration space. This trajectory-based theoretical framework is considered
here to study and analyze the outcome from Young-type diffraction experiments
within the context of the Arago-Fresnel laws. More specifically, photon
trajectories in the region behind the two slits are obtained in the case where
the slits are illuminated by a polarized monochromatic plane wave. Expressions
to determine electromagnetic energy flow lines and photon trajectories within
this scenario are provided, as well as a procedure to compute them in the
particular case of gratings totally transparent inside the slits and completely
absorbing outside them. As is shown, the electromagnetic energy flow lines
obtained allow to monitor at each point of space the behavior of the
electromagnetic energy flow and, therefore, to evaluate the effects caused on
it by the presence (right behind each slit) of polarizers with the same or
different polarization axes. This leads to a trajectory-based picture of the
Arago-Fresnel laws for the interference of polarized light.Comment: 36 pages, 6 figure
Should particle trajectories comply with the transverse momentum distribution?
The momentum distributions associated with both the wave function of a
particle behind a grating and the corresponding Bohmian trajectories are
investigated and compared. Near the grating, it is observed that the former
does not depend on the distance from the grating, while the latter changes with
this distance. However, as one moves further apart from the grating, in the far
field, both distributions become identical.Comment: 10 pages, 7 figure
Stochastic theory of lineshape broadening in quasielastic He atom scattering with interacting adsorbates
The activated surface diffusion of interacting adsorbates is described in
terms of the so-called interacting single adsorbate approximation, which is
applied to the diffusion of Na atoms on Cu(001) for coverages up to 20% in
quasielastic He atom scattering experiments. This approximation essentially
consists of solving the standard Langevin equation with two noise sources and
frictions: a Gaussian white noise accounting for the friction with the
substrate, and a white shot noise characterized by a collisional friction
simulating the adsorbate-adsorbate collisions. The broadenings undergone by the
quasielastic peak are found to be in very good agreement with the experimental
data reported at two surface temperatures 200 and 300 K.Comment: 6 pages, 3 figure