724 research outputs found
Composite absorbing potentials
The multiple scattering interferences due to the addition of several
contiguous potential units are used to construct composite absorbing potentials
that absorb at an arbitrary set of incident momenta or for a broad momentum
interval.Comment: 9 pages, Revtex, 2 postscript figures. Accepted in Phys. Rev. Let
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
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.
Real clocks and the Zeno effect
Real clocks are not perfect. This must have an effect in our predictions for
the behaviour of a quantum system, an effect for which we present a unified
description encompassing several previous proposals. We study the relevance of
clock errors in the Zeno effect, and find that generically no Zeno effect can
be present (in such a way that there is no contradiction with currently
available experimental data). We further observe that, within the class of
stochasticities in time addressed here, there is no modification in emission
lineshapes.Comment: 12 a4 pages, no figure
Free motion time-of-arrival operator and probability distribution
We reappraise and clarify the contradictory statements found in the
literature concerning the time-of-arrival operator introduced by Aharonov and
Bohm in Phys. Rev. {\bf 122}, 1649 (1961). We use Naimark's dilation theorem to
reproduce the generalized decomposition of unity (or POVM) from any
self-adjoint extension of the operator, emphasizing a natural one, which arises
from the analogy with the momentum operator on the half-line. General time
operators are set within a unifying perspective. It is shown that they are not
in general related to the time of arrival, even though they may have the same
form.Comment: 10 a4 pages, no figure
Time-of-arrival in quantum mechanics
We study the problem of computing the probability for the time-of-arrival of
a quantum particle at a given spatial position. We consider a solution to this
problem based on the spectral decomposition of the particle's (Heisenberg)
state into the eigenstates of a suitable operator, which we denote as the
``time-of-arrival'' operator. We discuss the general properties of this
operator. We construct the operator explicitly in the simple case of a free
nonrelativistic particle, and compare the probabilities it yields with the ones
estimated indirectly in terms of the flux of the Schr\"odinger current. We
derive a well defined uncertainty relation between time-of-arrival and energy;
this result shows that the well known arguments against the existence of such a
relation can be circumvented. Finally, we define a ``time-representation'' of
the quantum mechanics of a free particle, in which the time-of-arrival is
diagonal. Our results suggest that, contrary to what is commonly assumed,
quantum mechanics exhibits a hidden equivalence between independent (time) and
dependent (position) variables, analogous to the one revealed by the
parametrized formalism in classical mechanics.Comment: Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to
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
Controlling trapping potentials and stray electric fields in a microfabricated ion trap through design and compensation
Recent advances in quantum information processing with trapped ions have
demonstrated the need for new ion trap architectures capable of holding and
manipulating chains of many (>10) ions. Here we present the design and detailed
characterization of a new linear trap, microfabricated with scalable
complementary metal-oxide-semiconductor (CMOS) techniques, that is well-suited
to this challenge. Forty-four individually controlled DC electrodes provide the
many degrees of freedom required to construct anharmonic potential wells,
shuttle ions, merge and split ion chains, precisely tune secular mode
frequencies, and adjust the orientation of trap axes. Microfabricated
capacitors on DC electrodes suppress radio-frequency pickup and excess
micromotion, while a top-level ground layer simplifies modeling of electric
fields and protects trap structures underneath. A localized aperture in the
substrate provides access to the trapping region from an oven below, permitting
deterministic loading of particular isotopic/elemental sequences via
species-selective photoionization. The shapes of the aperture and
radio-frequency electrodes are optimized to minimize perturbation of the
trapping pseudopotential. Laboratory experiments verify simulated potentials
and characterize trapping lifetimes, stray electric fields, and ion heating
rates, while measurement and cancellation of spatially-varying stray electric
fields permits the formation of nearly-equally spaced ion chains.Comment: 17 pages (including references), 7 figure
Time in Quantum Mechanics and Quantum Field Theory
W. Pauli pointed out that the existence of a self-adjoint time operator is
incompatible with the semibounded character of the Hamiltonian spectrum. As a
result, people have been arguing a lot about the time-energy uncertainty
relation and other related issues. In this article, we show in details that
Pauli's definition of time operator is erroneous in several respects.Comment: 20 page
Time of arrival in the presence of interactions
We introduce a formalism for the calculation of the time of arrival t at a
space point for particles traveling through interacting media. We develop a
general formulation that employs quantum canonical transformations from the
free to the interacting cases to construct t in the context of the Positive
Operator Valued Measures. We then compute the probability distribution in the
times of arrival at a point for particles that have undergone reflection,
transmission or tunneling off finite potential barriers. For narrow Gaussian
initial wave packets we obtain multimodal time distributions of the reflected
packets and a combination of the Hartman effect with unexpected retardation in
tunneling. We also employ explicitly our formalism to deal with arrivals in the
interaction region for the step and linear potentials.Comment: 20 pages including 5 eps figure
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