114 research outputs found
Weak measurement of arrival time
The arrival time probability distribution is defined by analogy with the
classical mechanics. The difficulty of requirement to have the values of
non-commuting operators is circumvented using the concept of weak measurements.
The proposed procedure is suitable to the free particles and to the particles
subjected to an external potential, as well. It is shown that such an approach
imposes an inherent limitation to the accuracy of the arrival time
determination.Comment: 3 figure
Transient response of a quantum wave to an instantaneous potential step switching
The transient response of a stationary state of a quantum particle in a step
potential to an instantaneous change in the step height (a simplified model for
a sudden bias switch in an electronic semiconductor device) is solved exactly
by means of a semianalytical expression. The characteristic times for the
transient process up to the new stationary state are identified. A comparison
is made between the exact results and an approximate method.Comment: 8 pages, 8 figures, Revtex
Quantum times of arrival for multiparticle states
Using the concept of crossing state and the formalism of second quantization,
we propose a prescription for computing the density of arrivals of particles
for multiparticle states, both in the free and the interacting case. The
densities thus computed are positive, covariant in time for time independent
hamiltonians, normalized to the total number of arrivals, and related to the
flux. We investigate the behaviour of this prescriptions for bosons and
fermions, finding boson enhancement and fermion depletion of arrivals.Comment: 10 a4 pages, 5 inlined figure
Quantum-wave evolution in a step potential barrier
By using an exact solution to the time-dependent Schr\"{o}dinger equation
with a point source initial condition, we investigate both the time and spatial
dependence of quantum waves in a step potential barrier. We find that for a
source with energy below the barrier height, and for distances larger than the
penetration length, the probability density exhibits a {\it forerunner}
associated with a non-tunneling process, which propagates in space at exactly
the semiclassical group velocity. We show that the time of arrival of the
maximum of the {\it forerunner} at a given fixed position inside the potential
is exactly the traversal time, . We also show that the spatial evolution
of this transient pulse exhibits an invariant behavior under a rescaling
process. This analytic property is used to characterize the evolution of the
{\it forerunner}, and to analyze the role played by the time of arrival,
, found recently by Muga and B\"{u}ttiker [Phys. Rev. A {\bf 62},
023808 (2000)].Comment: To be published in Phys. Rev. A (2002
Consistent histories, the quantum Zeno effect, and time of arrival
We present a decomposition of the general quantum mechanical evolution
operator, that corresponds to the path decomposition expansion, and interpret
its constituents in terms of the quantum Zeno effect (QZE). This decomposition
is applied to a finite dimensional example and to the case of a free particle
in the real line, where the possibility of boundary conditions more general
than those hitherto considered in the literature is shown. We reinterpret the
assignment of consistent probabilities to different regions of spacetime in
terms of the QZE. The comparison of the approach of consistent histories to the
problem of time of arrival with the solution provided by the probability
distribution of Kijowski shows the strength of the latter point of view
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
Time-of-arrival distribution for arbitrary potentials and Wigner's time-energy uncertainty relation
A realization of the concept of "crossing state" invoked, but not
implemented, by Wigner, allows to advance in two important aspects of the time
of arrival in quantum mechanics: (i) For free motion, we find that the
limitations described by Aharonov et al. in Phys. Rev. A 57, 4130 (1998) for
the time-of-arrival uncertainty at low energies for certain mesurement models
are in fact already present in the intrinsic time-of-arrival distribution of
Kijowski; (ii) We have also found a covariant generalization of this
distribution for arbitrary potentials and positions.Comment: 4 pages, revtex, 2 eps figures include
The Time-Energy Uncertainty Relation
The time energy uncertainty relation has been a controversial issue since the
advent of quantum theory, with respect to appropriate formalisation, validity
and possible meanings. A comprehensive account of the development of this
subject up to the 1980s is provided by a combination of the reviews of Jammer
(1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are
concerned with different specific aspects of the subject. The purpose of this
chapter is to show that different types of time energy uncertainty relation can
indeed be deduced in specific contexts, but that there is no unique universal
relation that could stand on equal footing with the position-momentum
uncertainty relation. To this end, we will survey the various formulations of a
time energy uncertainty relation, with a brief assessment of their validity,
and along the way we will indicate some new developments that emerged since the
1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition
of "Time in quantum mechanics") contains minor corrections, new examples and
pointers to some additional relevant literatur
Matter wave pulses characteristics
We study the properties of quantum single-particle wave pulses created by
sharp-edged or apodized shutters with single or periodic openings. In
particular, we examine the visibility of diffraction fringes depending on
evolution time and temperature; the purity of the state depending on the
opening-time window; the accuracy of a simplified description which uses
``source'' boundary conditions instead of solving an initial value problem; and
the effects of apodization on the energy width.Comment: 11 pages, 11 figure
A novel presenilin 1 mutation (L174M) in a large Cuban family with early onset Alzheimer disease.
We studied a Cuban family with presenile dementia (autosomal dominant) consisting of 281 members within six generations, the proband descended from a Spanish founder. Mean age at onset was 59 years of age. Memory impairment was the main symptom in all patients, additionally, ischemic episodes were described in 4 (n = 18) patients. Neuropathological examination of brain material (1 patient) revealed neuronal loss, amyloid plaques, and neurofibrillary tangles. Thirty DNA samples were genotyped (regions on chromosome 1, 3, 10, 12, 14, 17, 19, 20, and 21). A maximum Lod score of 3.79 at theta = 0 was obtained for marker D14S43, located in a 9-cM interval in which all patients shared the same haplotype. Sequencing of the PSEN1 gene revealed a heterozygous base substitution, C520A (exon 6), which is predicted to cause an amino acid change from leucine to methionine in the TMIII of the presenilin 1 protein. The mutation was found to co-segregate with the disease phenotype and the associated disease haplotype. The C --> A change was not observed in 80 control chromosomes from the Cuban population. Leucine at position 174 is highly conserved among species and is identical in prese
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