3,541 research outputs found
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I
We exemplify the way the rigged Hilbert space deals with the
Lippmann-Schwinger equation by way of the spherical shell potential. We
explicitly construct the Lippmann-Schwinger bras and kets along with their
energy representation, their time evolution and the rigged Hilbert spaces to
which they belong. It will be concluded that the natural setting for the
solutions of the Lippmann-Schwinger equation--and therefore for scattering
theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur
Diversity of chemistry and excitation conditions in the high-mass star forming complex W33
The object W33 is a giant molecular cloud that contains star forming regions
at various evolutionary stages from quiescent clumps to developed H II regions.
Since its star forming regions are located at the same distance and the primary
material of the birth clouds is probably similar, we conducted a comparative
chemical study to trace the chemical footprint of the different phases of
evolution. We observed six clumps in W33 with the Atacama Pathfinder Experiment
(APEX) telescope at 280 GHz and the Submillimeter Array (SMA) at 230 GHz. We
detected 27 transitions of 10 different molecules in the APEX data and 52
transitions of 16 different molecules in the SMA data. The chemistry on scales
larger than 0.2 pc, which are traced by the APEX data, becomes more
complex and diverse the more evolved the star forming region is. On smaller
scales traced by the SMA data, the chemical complexity and diversity increase
up to the hot core stage. In the H II region phase, the SMA spectra resemble
the spectra of the protostellar phase. Either these more complex molecules are
destroyed or their emission is not compact enough to be detected with the SMA.
Synthetic spectra modelling of the HCO transitions, as detected with the
APEX telescope, shows that both a warm and a cold component are needed to
obtain a good fit to the emission for all sources except for W33 Main1. The
temperatures and column densities of the two components increase during the
evolution of the star forming regions. The integrated intensity ratios
NH(32)/CS(65) and
NH(32)/HCO(43) show clear trends as a
function of evolutionary stage, luminosity, luminosity-to-mass ratio, and
H peak column density of the clumps and might be usable as chemical
clocks.Comment: 66 pages, 28 figures, 8 tables, accepted for publication at A&
Robot’s weight distribution influence on angular momentum produced by a standing vertical jump
Vertical jump movement generators usually apply the ZMP (Zero Moment Point) and/or angular momentum equations as restrictions when planning the movements of the robot joints, which can cause undesired oscillations in the torso, compromise accuracy of the jump and/or complicate the search for online solutions. This paper presents a strategy to solve the problem related to angular momentum generated by the movement of the vertical jump, performed by a robot with 3 DoF (Degree of Freedom) and 4-links. Mentioned links correspond to the following parts of the human body: foot, leg, thigh and torso, and its weighted mass distribution and CoM (Center of Mass) position define an angular momentum profile within a specified range of speed values for the jump. In order for that to happen, simulations were performed using MATLAB, considering homogeneous and weighted distributions of total mass between the links of a robot and applying a third-degree polynomial function for the vertical acceleration curve of the CoM. The results suggest that based on the strategy proposed in this paper, it is possible to perform a vertical jump with dynamically stable movements and with angular moment near zero, and, at the same time, minimizing the problems presented in some prior methods. © 2016 IEEE.Vertical jump movement generators usually apply the ZMP (Zero Moment Point) and/or angular momentum equations as restrictions when planning the movements of the robot joints, which can cause undesired oscillations in the torso, compromise accuracy of the14416691676sem informaçãosem informaçã
On the inconsistency of the Bohm-Gadella theory with quantum mechanics
The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum
Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom
asserts that the solutions of the Lippmann-Schwinger equation are functionals
over spaces of Hardy functions. The preparation-registration arrow of time
provides the physical justification for the Hardy axiom. In this paper, it is
shown that the Hardy axiom is incorrect, because the solutions of the
Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also
shown that the derivation of the preparation-registration arrow of time is
flawed. Thus, Hardy functions neither appear when we solve the
Lippmann-Schwinger equation nor they should appear. It is also shown that the
Bohm-Gadella theory does not rest on the same physical principles as quantum
mechanics, and that it does not solve any problem that quantum mechanics cannot
solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page
The role of the rigged Hilbert space in Quantum Mechanics
There is compelling evidence that, when continuous spectrum is present, the
natural mathematical setting for Quantum Mechanics is the rigged Hilbert space
rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is
fully implemented by the rigged Hilbert space rather than just by the Hilbert
space. In this paper, we provide a pedestrian introduction to the role the
rigged Hilbert space plays in Quantum Mechanics, by way of a simple, exactly
solvable example. The procedure will be constructive and based on a recent
publication. We also provide a thorough discussion on the physical significance
of the rigged Hilbert space.Comment: 29 pages, 2 figures; a pedestrian introduction to the rigged Hilbert
spac
Stochastic Resonance in a Dipole
We show that the dipole, a system usually proposed to model relaxation
phenomena, exhibits a maximum in the signal-to-noise ratio at a non-zero noise
level, thus indicating the appearance of stochastic resonance. The phenomenon
occurs in two different situations, i.e. when the minimum of the potential of
the dipole remains fixed in time and when it switches periodically between two
equilibrium points. We have also found that the signal-to-noise ratio has a
maximum for a certain value of the amplitude of the oscillating field.Comment: 4 pages, RevTex, 6 PostScript figures available upon request; to
appear in Phys. Rev.
Rigged Hilbert Space Approach to the Schrodinger Equation
It is shown that the natural framework for the solutions of any Schrodinger
equation whose spectrum has a continuous part is the Rigged Hilbert Space
rather than just the Hilbert space. The difficulties of using only the Hilbert
space to handle unbounded Schrodinger Hamiltonians whose spectrum has a
continuous part are disclosed. Those difficulties are overcome by using an
appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an
eigenket to each energy in the spectrum of the Hamiltonian, regardless of
whether the energy belongs to the discrete or to the continuous part of the
spectrum. The collection of eigenkets corresponding to both discrete and
continuous spectra forms a basis system that can be used to expand any physical
wave function. Thus the RHS treats discrete energies (discrete spectrum) and
scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page
Stochastic Resonance in Nonpotential Systems
We propose a method to analytically show the possibility for the appearance
of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our
results to the FitzHugh-Nagumo model under a periodic external forcing, showing
that the model exhibits stochastic resonance. The procedure that we follow is
based on the reduction to a one-dimensional dynamics in the adiabatic limit,
and in the topology of the phase space of the systems under study. Its
application to other nonpotential systems is also discussed.Comment: Submitted to Phys. Rev.
Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
We aim to clarify confusions in the literature as to whether or not dynamical
density functional theories for the one-body density of a classical Brownian
fluid should contain a stochastic noise term. We point out that a stochastic as
well as a deterministic equation of motion for the density distribution can be
justified, depending on how the fluid one-body density is defined -- i.e.
whether it is an ensemble averaged density distribution or a spatially and/or
temporally coarse grained density distribution.Comment: 10 pages, 1 figure, to be submitted to Journal of Physics A:
Mathematical and Genera
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