82 research outputs found
Phase shift effective range expansion from supersymmetric quantum mechanics
Supersymmetric or Darboux transformations are used to construct local phase
equivalent deep and shallow potentials for partial waves. We
associate the value of the orbital angular momentum with the asymptotic form of
the potential at infinity which allows us to introduce adequate long-distance
transformations. The approach is shown to be effective in getting the correct
phase shift effective range expansion. Applications are considered for the
and partial waves of the neutron-proton scattering.Comment: 6 pages, 3 figures, Revtex4, version to be publised in Physical
Review
Eigenphase preserving two-channel SUSY transformations
We propose a new kind of supersymmetric (SUSY) transformation in the case of
the two-channel scattering problem with equal thresholds, for partial waves of
the same parity. This two-fold transformation is based on two imaginary
factorization energies with opposite signs and with mutually conjugated
factorization solutions. We call it an eigenphase preserving SUSY
transformation as it relates two Hamiltonians, the scattering matrices of which
have identical eigenphase shifts. In contrast to known phase-equivalent
transformations, the mixing parameter is modified by the eigenphase preserving
transformation.Comment: 16 pages, 1 figur
Equivalence of the Siegert-pseudostate and Lagrange-mesh R-matrix methods
Siegert pseudostates are purely outgoing states at some fixed point expanded
over a finite basis. With discretized variables, they provide an accurate
description of scattering in the s wave for short-range potentials with few
basis states. The R-matrix method combined with a Lagrange basis, i.e.
functions which vanish at all points of a mesh but one, leads to simple
mesh-like equations which also allow an accurate description of scattering.
These methods are shown to be exactly equivalent for any basis size, with or
without discretization. The comparison of their assumptions shows how to
accurately derive poles of the scattering matrix in the R-matrix formalism and
suggests how to extend the Siegert-pseudostate method to higher partial waves.
The different concepts are illustrated with the Bargmann potential and with the
centrifugal potential. A simplification of the R-matrix treatment can usefully
be extended to the Siegert-pseudostate method.Comment: 19 pages, 1 figur
Coherent Backscattering of light in a magnetic field
This paper describes how coherent backscattering is altered by an external
magnetic field. In the theory presented, magneto-optical effects occur inside
Mie scatterers embedded in a non-magnetic medium. Unlike previous theories
based on point-like scatterers, the decrease of coherent backscattering is
obtained in leading order of the magnetic field using rigorous Mie theory. This
decrease is strongly enhanced in the proximity of resonances, which cause the
path length of the wave inside a scatterer to be increased. Also presented is a
novel analysis of the shape of the backscattering cone in a magnetic field.Comment: 27 pages, 5 figures, Revtex, to appear in Phys. Rev.
Single- and coupled-channel radial inverse scattering with supersymmetric transformations
The present status of the coupled-channel inverse-scattering method with
supersymmetric transformations is reviewed. We first revisit in a pedagogical
way the single-channel case, where the supersymmetric approach is shown to
provide a complete solution to the inverse-scattering problem. A special
emphasis is put on the differences between conservative and non-conservative
transformations. In particular, we show that for the zero initial potential, a
non-conservative transformation is always equivalent to a pair of conservative
transformations. These single-channel results are illustrated on the inversion
of the neutron-proton triplet eigenphase shifts for the S and D waves. We then
summarize and extend our previous works on the coupled-channel case and stress
remaining difficulties and open questions. We mostly concentrate on two-channel
examples to illustrate general principles while keeping mathematics as simple
as possible. In particular, we discuss the difference between the
equal-threshold and different-threshold problems. For equal thresholds,
conservative transformations can provide non-diagonal Jost and scattering
matrices. Iterations of such transformations are shown to lead to practical
algorithms for inversion. A convenient technique where the mixing parameter is
fitted independently of the eigenphases is developed with iterations of pairs
of conjugate transformations and applied to the neutron-proton triplet S-D
scattering matrix, for which exactly-solvable matrix potential models are
constructed. For different thresholds, conservative transformations do not seem
to be able to provide a non-trivial coupling between channels. In contrast, a
single non-conservative transformation can generate coupled-channel potentials
starting from the zero potential and is a promising first step towards a full
solution to the coupled-channel inverse problem with threshold differences.Comment: Topical review, 84 pages, 7 figures, 93 reference
Do experts see it in slow motion? Altered timing of action simulation uncovers domain-specific perceptual processing in expert athletes
Accurate encoding of the spatio-temporal properties of others' actions is essential for the successful implementation of daily activities and, even more, for successful sportive performance, given its role in movement coordination and action anticipation. Here we investigated whether athletes are provided with special perceptual processing of spatio-temporal properties of familiar sportive actions. Basketball and volleyball players and novices were presented with short video-clips of free basketball throws that were partially occluded ahead of realization and were asked to judge whether a subsequently presented pose was either taken from the same throw depicted in the occluded video (action identification task) or temporally congruent with the expected course of the action during the occlusion period (explicit timing task). Results showed that basketball players outperformed the other groups in detecting action compatibility when the pose depicted earlier or synchronous, but not later phases of the movement as compared to the natural course of the action during occlusion. No difference was obtained for explicit estimations of timing compatibility. This leads us to argue that the timing of simulated actions in the experts might be slower than that of perceived actions ("slow-motion" bias), allowing for more detailed representation of ongoing actions and refined prediction abilities
Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
Nonlinear SUSY approach to preparation of quantum systems with pre-planned
spectral properties is reviewed. Possible multidimensional extensions of
Nonlinear SUSY are described. The full classification of ladder-reducible and
irreducible chains of SUSY algebras in one-dimensional QM is given. Emergence
of hidden symmetries and spectrum generating algebras is elucidated in the
context of Nonlinear SUSY in one- and two-dimensional QM.Comment: 75 pages, Minor corrections, Version published in Journal of Physics
Group membership and racial bias modulate the temporal estimation of in-group/out-group body movements
Social group categorization has been mainly studied in relation to ownership manipulations involving highly-salient multisensory cues. Here, we propose a novel paradigm that can implicitly activate the embodiment process in the presence of group affiliation information, whilst participants complete a task irrelevant to social categorization. Ethnically White participants watched videos of White- and Black-skinned models writing a proverb. The writing was interrupted 7, 4 or 1 s before completion. Participants were tasked with estimating the residual duration following interruption. A video showing only hand kinematic traces acted as a control condition. Residual duration estimates for out-group and control videos were significantly lower than those for in-group videos only for the longest duration. Moreover, stronger implicit racial bias was negatively correlated to estimates of residual duration for out-group videos. The underestimation bias for the out-group condition might be mediated by implicit embodiment, affective and attentional processes, and finalized to a rapid out-group categorization
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