281 research outputs found
Object-oriented Programming Laws for Annotated Java Programs
Object-oriented programming laws have been proposed in the context of
languages that are not combined with a behavioral interface specification
language (BISL). The strong dependence between source-code and interface
specifications may cause a number of difficulties when transforming programs.
In this paper we introduce a set of programming laws for object-oriented
languages like Java combined with the Java Modeling Language (JML). The set of
laws deals with object-oriented features taking into account their
specifications. Some laws deal only with features of the specification
language. These laws constitute a set of small transformations for the
development of more elaborate ones like refactorings
Probability distribution of arrival times in quantum mechanics
In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)]
we introduced a self-adjoint operator whose eigenstates
can be used to define consistently a probability distribution of the time of
arrival at a given spatial point. In the present work we show that the
probability distribution previously proposed can be well understood on
classical grounds in the sense that it is given by the expectation value of a
certain positive definite operator which is nothing but a
straightforward quantum version of the modulus of the classical current. For
quantum states highly localized in momentum space about a certain momentum , the expectation value of becomes indistinguishable
from the quantum probability current. This fact may provide a justification for
the common practice of using the latter quantity as a probability distribution
of arrival times.Comment: 21 pages, LaTeX, no figures; A Note added; To be published in Phys.
Rev.
Tunneling Time in the Landau-Zener Model
We give a general definition for the tunneling time in the Landau-Zener
model. This definition allows us to compute numerically the Landau-Zener
tunneling time at any sweeping rate without ambiguity. We have also obtained
analytical results in both the adiabatic limit and the sudden limit. Whenever
applicable, our results are compared to previous results and they are in good
agreement.Comment: 7pages, 9 figure
Possibility of the tunneling time determination
We show that it is impossible to determine the time a tunneling particle
spends under the barrier. However, it is possible to determine the asymptotic
time, i.e., the time the particle spends in a large area including the barrier.
We propose a model of time measurements. The model provides a procedure for
calculation of the asymptotic tunneling and reflection times. The model also
demonstrates the impossibility of determination of the time the tunneling
particle spends under the barrier. Examples for delta-form and rectangular
barrier illustrate the obtained results.Comment: 8 figure
Strong quantum violation of the gravitational weak equivalence principle by a non-Gaussian wave-packet
The weak equivalence principle of gravity is examined at the quantum level in
two ways. First, the position detection probabilities of particles described by
a non-Gaussian wave-packet projected upwards against gravity around the
classical turning point and also around the point of initial projection are
calculated. These probabilities exhibit mass-dependence at both these points,
thereby reflecting the quantum violation of the weak equivalence principle.
Secondly, the mean arrival time of freely falling particles is calculated using
the quantum probability current, which also turns out to be mass dependent.
Such a mass-dependence is shown to be enhanced by increasing the
non-Gaussianity parameter of the wave packet, thus signifying a stronger
violation of the weak equivalence principle through a greater departure from
Gaussianity of the initial wave packet. The mass-dependence of both the
position detection probabilities and the mean arrival time vanish in the limit
of large mass. Thus, compatibility between the weak equivalence principle and
quantum mechanics is recovered in the macroscopic limit of the latter. A
selection of Bohm trajectories is exhibited to illustrate these features in the
free fall case.Comment: 11 pages, 7 figure
Time-of-arrival formalism for the relativistic particle
A suitable operator for the time-of-arrival at a detector is defined for the
free relativistic particle in 3+1 dimensions. For each detector position, there
exists a subspace of detected states in the Hilbert space of solutions to the
Klein Gordon equation. Orthogonality and completeness of the eigenfunctions of
the time-of-arrival operator apply inside this subspace, opening up a standard
probabilistic interpretation.Comment: 16 pages, no figures, uses LaTeX. The section "Interpretation" has
been completely rewritten and some errors correcte
Diffraction in time of a confined particle and its Bohmian paths
Diffraction in time of a particle confined in a box which its walls are
removed suddenly at is studied. The solution of the time-dependent
Schr\"{o}dinger equation is discussed analytically and numerically for various
initial wavefunctions. In each case Bohmian trajectories of the particles are
computed and also the mean arrival time at a given location is studied as a
function of the initial state.Comment: 8 pages, 6 figure
Renormalization group approach to anisotropic superconductivity
The superconducting instability of the Fermi liquid state is investigated by
considering anisotropic electron-boson couplings. Both electron-electron
interactions and anisotropic electron-boson couplings are treated with a
renormalization-group method that takes into account retardation effects.
Considering a non-interacting circular Fermi surface, we find analytical
solutions for the flow equations and derive a set of generalized Eliashberg
equations. Electron-boson couplings with different momentum dependences are
studied, and we find superconducting instabilities of the metallic state with
competition between order parameters of different symmetries. Numerical
solutions for some couplings are given to illustrate the frequency dependence
of the vertices at different coupling regimes.Comment: 9 pages, 7 figures. Final version as published in Phys. Rev.
Quantum probability distribution of arrival times and probability current density
This paper compares the proposal made in previous papers for a quantum
probability distribution of the time of arrival at a certain point with the
corresponding proposal based on the probability current density. Quantitative
differences between the two formulations are examined analytically and
numerically with the aim of establishing conditions under which the proposals
might be tested by experiment. It is found that quantum regime conditions
produce the biggest differences between the formulations which are otherwise
near indistinguishable. These results indicate that in order to discriminate
conclusively among the different alternatives, the corresponding experimental
test should be performed in the quantum regime and with sufficiently high
resolution so as to resolve small quantum efects.Comment: 21 pages, 7 figures, LaTeX; Revised version to appear in Phys. Rev. A
(many small changes
Correcting the quantum clock: conditional sojourn times
Can the quantum-mechanical sojourn time be clocked without the clock
affecting the sojourn time? Here we re-examine the previously proposed
non-unitary clock, involving absorption/amplification by an added infinitesimal
imaginary potential(), and find it {\it not} to preserve, in general,
the positivity of the sojourn time, conditional on eventual reflection or
transmission. The sojourn time is found to be affected by the scattering
concomitant with the mismatch, however small, due to the very clock
potential() introduced for the purpose, as also by any prompt
scattering involving partial waves that have not traversed the region of
interest. We propose a formal procedure whereby the sojourn time so clocked can
be corrected for these spurious scattering effects. The resulting conditional
sojourn times are then positive definite for an arbitrary potential, and have
the proper high- and low-energy limits.Comment: Corrected and rewritten, RevTeX, 4 pages, 2 figures (ps files)
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