36 research outputs found
Generalized definition of time delay in scattering theory
We advocate for the systematic use of a symmetrized definition of time delay
in scattering theory. In two-body scattering processes, we show that the
symmetrized time delay exists for arbitrary dilated spatial regions symmetric
with respect to the origin. It is equal to the usual time delay plus a new
contribution, which vanishes in the case of spherical spatial regions. We also
prove that the symmetrized time delay is invariant under an appropriate mapping
of time reversal. These results are also discussed in the context of classical
scattering theory.Comment: 18 page
Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aert's machine-models
From the beginning of his research, the Belgian physicist Diederik Aerts has
shown great creativity in inventing a number of concrete machine-models that
have played an important role in the development of general mathematical and
conceptual formalisms for the description of the physical reality. These models
can also be used to demystify much of the strangeness in the behavior of
quantum entities, by allowing to have a peek at what's going on - in structural
terms - behind the "quantum scenes," during a measurement. In this author's
view, the importance of these machine-models, and of the approaches they have
originated, have been so far seriously underappreciated by the physics
community, despite their success in clarifying many challenges of quantum
physics. To fill this gap, and encourage a greater number of researchers to
take cognizance of the important work of so-called Geneva-Brussels school, we
describe and analyze in this paper two of Aerts' historical machine-models,
whose operations are based on simple breakable elastic bands. The first one,
called the spin quantum-machine, is able to replicate the quantum probabilities
associated with the spin measurement of a spin-1/2 entity. The second one,
called the \emph{connected vessels of water model} (of which we shall present
here an alternative version based on elastics) is able to violate Bell's
inequality, as coincidence measurements on entangled states can do.Comment: 15 pages, 5 figure
Transmission resonances and supercritical states in a one dimensional cusp potential
We solve the two-component Dirac equation in the presence of a spatially one
dimensional symmetric cusp potential. We compute the scattering and bound
states solutions and we derive the conditions for transmission resonances as
well as for supercriticality.Comment: 10 pages. Revtex 4. To appear in Phys Rev.
Time delay for one-dimensional quantum systems with steplike potentials
This paper concerns time-dependent scattering theory and in particular the
concept of time delay for a class of one-dimensional anisotropic quantum
systems. These systems are described by a Schr\"{o}dinger Hamiltonian with a potential converging to different limits
and as and respectively. Due to the
anisotropy they exhibit a two-channel structure. We first establish the
existence and properties of the channel wave and scattering operators by using
the modern Mourre approach. We then use scattering theory to show the identity
of two apparently different representations of time delay. The first one is
defined in terms of sojourn times while the second one is given by the
Eisenbud-Wigner operator. The identity of these representations is well known
for systems where vanishes as (). We show
that it remains true in the anisotropic case , i.e. we prove
the existence of the time-dependent representation of time delay and its
equality with the time-independent Eisenbud-Wigner representation. Finally we
use this identity to give a time-dependent interpretation of the
Eisenbud-Wigner expression which is commonly used for time delay in the
literature.Comment: 48 pages, 1 figur
A single-mode quantum transport in serial-structure geometric scatterers
We study transport in quantum systems consisting of a finite array of N
identical single-channel scatterers. A general expression of the S matrix in
terms of the individual-element data obtained recently for potential scattering
is rederived in this wider context. It shows in particular how the band
spectrum of the infinite periodic system arises in the limit . We
illustrate the result on two kinds of examples. The first are serial graphs
obtained by chaining loops or T-junctions. A detailed discussion is presented
for a finite-periodic "comb"; we show how the resonance poles can be computed
within the Krein formula approach. Another example concerns geometric
scatterers where the individual element consists of a surface with a pair of
leads; we show that apart of the resonances coming from the decoupled-surface
eigenvalues such scatterers exhibit the high-energy behavior typical for the
delta' interaction for the physically interesting couplings.Comment: 36 pages, a LaTeX source file with 2 TeX drawings, 3 ps and 3 jpeg
figures attache
Ephemeral properties and the illusion of microscopic particles
Founding our analysis on the Geneva-Brussels approach to quantum mechanics,
we use conventional macroscopic objects as guiding examples to clarify the
content of two important results of the beginning of twentieth century:
Einstein-Podolsky-Rosen's reality criterion and Heisenberg's uncertainty
principle. We then use them in combination to show that our widespread belief
in the existence of microscopic particles is only the result of a cognitive
illusion, as microscopic particles are not particles, but are instead the
ephemeral spatial and local manifestations of non-spatial and non-local
entities
The Generalized Star Product and the Factorization of Scattering Matrices on Graphs
In this article we continue our analysis of Schr\"odinger operators on
arbitrary graphs given as certain Laplace operators. In the present paper we
give the proof of the composition rule for the scattering matrices. This
composition rule gives the scattering matrix of a graph as a generalized star
product of the scattering matrices corresponding to its subgraphs. We perform a
detailed analysis of the generalized star product for arbitrary unitary
matrices. The relation to the theory of transfer matrices is also discussed
How much time does a tunneling particle spend in the barrier region?
The question in the title may be answered by considering the outcome of a
``weak measurement'' in the sense of Aharonov et al. Various properties of the
resulting time are discussed, including its close relation to the Larmor times.
It is a universal description of a broad class of measurement interactions, and
its physical implications are unambiguous.Comment: 5 pages; no figure
The delta-quantum machine, the k-model, and the non-ordinary spatiality of quantum entities
The purpose of this article is threefold. Firstly, it aims to present, in an
educational and non-technical fashion, the main ideas at the basis of Aerts'
creation-discovery view and hidden measurement approach: a fundamental
explanatory framework whose importance, in this author's view, has been
seriously underappreciated by the physics community, despite its success in
clarifying many conceptual challenges of quantum physics. Secondly, it aims to
introduce a new quantum-machine - that we call the delta-quantum-machine -
which is able to reproduce the transmission and reflection probabilities of a
one-dimensional quantum scattering process by a Dirac delta-function potential.
The machine is used not only to demonstrate the pertinence of the above
mentioned explanatory framework, in the general description of physical
systems, but also to illustrate (in the spirit of Aerts' epsilon-model) the
origin of classical and quantum structures, by revealing the existence of
processes which are neither classical nor quantum, but irreducibly
intermediate. We do this by explicitly introducing what we call the k-model and
by proving that its processes cannot be modelized by a classical or quantum
scattering system. The third purpose of this work is to exploit the powerful
metaphor provided by our quantum-machine, to investigate the intimate relation
between the concept of potentiality and the notion of non-spatiality, that we
characterize in precise terms, introducing for this the new concept of
process-actuality.Comment: 19 pages, 4 figures. To appear in: Foundations of Scienc