64 research outputs found
Rediscovering Sculptures from Tebtynis at the Museo Egizio in Turin
This article presents three case studies from an ongoing research project on the statues and sculptural fragments from Tebtynis, discovered by Carlo Anti in the years 1930-1936 in the temple dedicated to the god Soknebtynis. Specifically, it examines the following three statues: Alexandria, Graeco-Roman Museum inv. no. 22979, Turin, Museo Egizio S. 18176, and a non-royal statue which one of the authors has recently identified as Turin, Museo Egizio S. 19400+S. 19400/1. The authors combine stylistic analysis with a study of relevant archival records currently kept in Padua and Venice, Italy, to shed light on these sculptures and retrace their
post-excavation history
A New Supersymmetric Extension of Conformal Mechanics
In this paper a new supersymmetric extension of conformal mechanics is put
forward. The beauty of this extension is that all variables have a clear
geometrical meaning and the super-Hamiltonian turns out to be the
Lie-derivative of the Hamiltonian flow of standard conformal mechanics. In this
paper we also provide a supersymmetric extension of the other conformal
generators of the theory and find their "square-roots". The whole superalgebra
of these charges is then analyzed in details. We conclude the paper by showing
that, using superfields, a constraint can be built which provides the exact
solution of the system.Comment: 11 pages, no figure
A New Superconformal Mechanics
In this paper we propose a new supersymmetric extension of conformal
mechanics. The Grassmannian variables that we introduce are the basis of the
forms and of the vector-fields built over the symplectic space of the original
system. Our supersymmetric Hamiltonian itself turns out to have a clear
geometrical meaning being the Lie-derivative of the Hamiltonian flow of
conformal mechanics. Using superfields we derive a constraint which gives the
exact solution of the supersymmetric system in a way analogous to the
constraint in configuration space which solved the original non-supersymmetric
model. Besides the supersymmetric extension of the original Hamiltonian, we
also provide the extension of the other conformal generators present in the
original system. These extensions have also a supersymmetric character being
the square of some Grassmannian charge. We build the whole superalgebra of
these charges and analyze their closure. The representation of the even part of
this superalgebra on the odd part turns out to be integer and not spinorial in
character.Comment: Superfield re-define
Typicality vs. probability in trajectory-based formulations of quantum mechanics
Bohmian mechanics represents the universe as a set of paths with a
probability measure defined on it. The way in which a mathematical model of
this kind can explain the observed phenomena of the universe is examined in
general. It is shown that the explanation does not make use of the full
probability measure, but rather of a suitable set function deriving from it,
which defines relative typicality between single-time cylinder sets. Such a set
function can also be derived directly from the standard quantum formalism,
without the need of an underlying probability measure. The key concept for this
derivation is the {\it quantum typicality rule}, which can be considered as a
generalization of the Born rule. The result is a new formulation of quantum
mechanics, in which particles follow definite trajectories, but which is only
based on the standard formalism of quantum mechanics.Comment: 24 pages, no figures. To appear in Foundation of Physic
Ambiguities of arrival-time distributions in quantum theory
We consider the definition that might be given to the time at which a
particle arrives at a given place, both in standard quantum theory and also in
Bohmian mechanics. We discuss an ambiguity that arises in the standard theory
in three, but not in one, spatial dimension.Comment: LaTex, 12 pages, no figure
Implications of Lorentz covariance for the guidance equation in two-slit quantum interference
It is known that Lorentz covariance fixes uniquely the current and the
associated guidance law in the trajectory interpretation of quantum mechanics
for spin particles. In the non-relativistic domain this implies a guidance law
for the electron which differs by an additional spin-dependent term from that
originally proposed by de Broglie and Bohm. In this paper we explore some of
the implications of the modified guidance law. We bring out a property of
mutual dependence in the particle coordinates that arises in product states,
and show that the quantum potential has scalar and vector components which
implies the particle is subject to a Lorentz-like force. The conditions for the
classical limit and the limit of negligible spin are given, and the empirical
sufficiency of the model is demonstrated. We then present a series of
calculations of the trajectories based on two-dimensional Gaussian wave packets
which illustrate how the additional spin-dependent term plays a significant
role in structuring both the individual trajectories and the ensemble. The
single packet corresponds to quantum inertial motion. The distinct features
encountered when the wavefunction is a product or a superposition are explored,
and the trajectories that model the two-slit experiment are given. The latter
paths exhibit several new characteristics compared with the original de
Broglie-Bohm ones, such as crossing of the axis of symmetry.Comment: 27 pages including 6 pages of figure
The classical supersymmetric Coulomb problem
After setting up a general model for supersymmetric classical mechanics in
more than one dimension we describe systems with centrally symmetric potentials
and their Poisson algebra. We then apply this information to the investigation
and solution of the supersymmetric Coulomb problem, specified by an 1/|x|
repulsive bosonic potential.Comment: 25 pages, 2 figures; reference added, some minor modification
Spin dependent observable effect for free particles using the arrival time distribution
The mean arrival time of free particles is computed using the quantum
probability current. This is uniquely determined in the non-relativistic limit
of Dirac equation, although the Schroedinger probability current has an
inherent non-uniqueness. Since the Dirac probability current involves a
spin-dependent term, an arrival time distribution based on the probability
current shows an observable spin-dependent effect, even for free particles.
This arises essentially from relativistic quantum dynamics, but persists even
in the non-relativistic regime.Comment: 5 Latex pages, 2.eps figures; discussions sharpened and references
added; accepted for publication in Physical Review
Quantum random walks with history dependence
We introduce a multi-coin discrete quantum random walk where the amplitude
for a coin flip depends upon previous tosses. Although the corresponding
classical random walk is unbiased, a bias can be introduced into the quantum
walk by varying the history dependence. By mixing the biased random walk with
an unbiased one, the direction of the bias can be reversed leading to a new
quantum version of Parrondo's paradox.Comment: 8 pages, 6 figures, RevTe
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