63 research outputs found
Comment on "Foundations of quantum mechanics: Connection with stochastic processes"
Recently, Olavo has proposed several derivations of the Schrodinger equation
from different sets of hypothesis ("axiomatizations") [Phys. Rev. A 61, 052109
(2000)]. One of them is based on the infinitesimal inverse Weyl transform of a
classically evolved phase space density. We show however that the Schrodinger
equation can only be obtained in that manner for linear or quadratic potential
functions.Comment: 3 pages, no figure
Quantum arrival time measurement and backflow effect
The current density for a freely evolving state without negative momentum
components can temporarily be negative. The operational arrival time
distribution, defined by the absorption rate of an ideal detector, is
calculated for a model detector and compared with recently proposed
distributions. Counterintuitive features of the backflow regime are discussed.Comment: LATEX, 9 pages, 2 postscript 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 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
Scattering by PT-symmetric non-local potentials
A general formalism is worked out for the description of one-dimensional
scattering by non-local separable potentials and constraints on transmission
and reflection coefficients are derived in the cases of P, T, or PT invariance
of the Hamiltonian. The case of a solvable Yamaguchi potential is discussed in
detail.Comment: 11 page
Time-of-arrival distributions from position-momentum and energy-time joint measurements
The position-momentum quasi-distribution obtained from an Arthurs and Kelly
joint measurement model is used to obtain indirectly an ``operational''
time-of-arrival (TOA) distribution following a quantization procedure proposed
by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA
distribution is not time covariant. The procedure is generalized by using other
phase-space quasi-distributions, and sufficient conditions are provided for
time covariance that limit the possible phase-space quasi-distributions
essentially to the Wigner function, which, however, provides a non-positive TOA
quasi-distribution. These problems are remedied with a different quantization
procedure which, on the other hand, does not guarantee normalization. Finally
an Arthurs and Kelly measurement model for TOA and energy (valid also for
arbitrary conjugate variables when one of the variables is bounded from below)
is worked out. The marginal TOA distribution so obtained, a distorted version
of Kijowski's distribution, is time covariant, positive, and normalized
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
Dwell-time distributions in quantum mechanics
Some fundamental and formal aspects of the quantum dwell time are reviewed,
examples for free motion and scattering off a potential barrier are provided,
as well as extensions of the concept. We also examine the connection between
the dwell time of a quantum particle in a region of space and flux-flux
correlations at the boundaries, as well as operational approaches and
approximations to measure the flux-flux correlation function and thus the
second moment of the dwell time, which is shown to be characteristically
quantum, and larger than the corresponding classical moment even for freely
moving particles.Comment: To appear in "Time in Quantum Mechanics, Vol. 2", Springer 2009, ed.
by J. G. Muga, A. Ruschhaupt and A. del Camp
Ultra-fast propagation of Schr\"odinger waves in absorbing media
We identify the characteristic times of the evolution of a quantum wave
generated by a point source with a sharp onset in an absorbing medium. The
"traversal'' or "B\"uttiker-Landauer'' time (which grows linearly with the
distance to the source) for the Hermitian, non-absorbing case is substituted by
three different characteristic quantities. One of them describes the arrival of
a maximum of the density calculated with respect to position, but the maximum
with respect to time for a given position becomes independent of the distance
to the source and is given by the particle's ``survival time'' in the medium.
This later effect, unlike the Hartman effect, occurs for injection frequencies
under or above the cut-off, and for arbitrarily large distances. A possible
physical realization is proposed by illuminating a two-level atom with a
detuned laser
Time of arrival through interacting environments: Tunneling processes
We discuss the propagation of wave packets through interacting environments.
Such environments generally modify the dispersion relation or shape of the wave
function. To study such effects in detail, we define the distribution function
P_{X}(T), which describes the arrival time T of a packet at a detector located
at point X. We calculate P_{X}(T) for wave packets traveling through a
tunneling barrier and find that our results actually explain recent
experiments. We compare our results with Nelson's stochastic interpretation of
quantum mechanics and resolve a paradox previously apparent in Nelson's
viewpoint about the tunneling time.Comment: Latex 19 pages, 11 eps figures, title modified, comments and
references added, final versio
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