301 research outputs found
The norm-1-property of a quantum observable
A normalized positive operator measure has the
norm-1-property if \no{E(X)}=1 whenever . This property reflects
the fact that the measurement outcome probabilities for the values of such
observables can be made arbitrary close to one with suitable state
preparations. Some general implications of the norm-1-property are
investigated. As case studies, localization observables, phase observables, and
phase space observables are considered.Comment: 14 page
Generalizations of Kijowski's time-of-arrival distribution for interaction potentials
Several proposals for a time-of-arrival distribution of ensembles of
independent quantum particles subject to an external interaction potential are
compared making use of the ``crossing state'' concept. It is shown that only
one of them has the properties expected for a classical distribution in the
classical limit. The comparison is illustrated numerically with a collision of
a Gaussian wave packet with an opaque square barrier.Comment: 5 inlined figures: some typo correction
Quantum physics in inertial and gravitational fields
Covariant generalizations of well-known wave equations predict the existence
of inertial-gravitational effects for a variety of quantum systems that range
from Bose-Einstein condensates to particles in accelerators. Additional effects
arise in models that incorporate Born reciprocity principle and the notion of a
maximal acceleration. Some specific examples are discussed in detail.Comment: 25 pages,1 figure,to appear in "Relativity in Rotating Frame
Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique
We present a Master equation for description of fermions and bosons for
special relativities with two invariant scales, SR2, (c and lambda_P). We
introduce canonically-conjugate variables (chi^0, chi) to (epsilon, pi) of
Judes-Visser. Together, they bring in a formal element of linearity and
locality in an otherwise non-linear and non-local theory. Special relativities
with two invariant scales provide all corrections, say, to the standard model
of the high energy physics, in terms of one fundamental constant, lambda_P. It
is emphasized that spacetime of special relativities with two invariant scales
carries an intrinsic quantum-gravitational character. In an addenda, we also
comment on the physical importance of a phase factor that the whole literature
on the subject has missed and present a brief critique of SR2. In addition, we
remark that the most natural and physically viable SR2 shall require
momentum-space and spacetime to be non-commutative with the non-commutativity
determined by the spin content and C, P, and T properties of the examined
representation space. Therefore, in a physically successful SR2, the notion of
spacetime is expected to be deeply intertwined with specific properties of the
test particle.Comment: Int. J. Mod. Phys. D (in press). Extended version of a set of two
informal lectures given in "La Sapienza" (Rome, May 2001
Field on Poincare group and quantum description of orientable objects
We propose an approach to the quantum-mechanical description of relativistic
orientable objects. It generalizes Wigner's ideas concerning the treatment of
nonrelativistic orientable objects (in particular, a nonrelativistic rotator)
with the help of two reference frames (space-fixed and body-fixed). A technical
realization of this generalization (for instance, in 3+1 dimensions) amounts to
introducing wave functions that depend on elements of the Poincare group . A
complete set of transformations that test the symmetries of an orientable
object and of the embedding space belongs to the group . All
such transformations can be studied by considering a generalized regular
representation of in the space of scalar functions on the group, ,
that depend on the Minkowski space points as well as on the
orientation variables given by the elements of a matrix .
In particular, the field is a generating function of usual spin-tensor
multicomponent fields. In the theory under consideration, there are four
different types of spinors, and an orientable object is characterized by ten
quantum numbers. We study the corresponding relativistic wave equations and
their symmetry properties.Comment: 46 page
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
Localization of Events in Space-Time
The present paper deals with the quantum coordinates of an event in
space-time, individuated by a quantum object. It is known that these
observables cannot be described by self-adjoint operators or by the
corresponding spectral projection-valued measure. We describe them by means of
a positive-operator-valued (POV) measure in the Minkowski space-time,
satisfying a suitable covariance condition with respect to the Poincare' group.
This POV measure determines the probability that a measurement of the
coordinates of the event gives results belonging to a given set in space-time.
We show that this measure must vanish on the vacuum and the one-particle
states, which cannot define any event. We give a general expression for the
Poincare' covariant POV measures. We define the baricentric events, which lie
on the world-line of the centre-of-mass, and we find a simple expression for
the average values of their coordinates. Finally, we discuss the conditions
which permit the determination of the coordinates with an arbitrary accuracy.Comment: 31 pages, latex, no figure
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
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
Toy Model for a Relational Formulation of Quantum Theory
In the absence of an external frame of reference physical degrees of freedom
must describe relations between systems. Using a simple model, we investigate
how such a relational quantum theory naturally arises by promoting reference
systems to the status of dynamical entities. Our goal is to demonstrate using
elementary quantum theory how any quantum mechanical experiment admits a purely
relational description at a fundamental level, from which the original
"non-relational" theory emerges in a semi-classical limit. According to this
thesis, the non-relational theory is therefore an approximation of the
fundamental relational theory. We propose four simple rules that can be used to
translate an "orthodox" quantum mechanical description into a relational
description, independent of an external spacial reference frame or clock. The
techniques used to construct these relational theories are motivated by a
Bayesian approach to quantum mechanics, and rely on the noiseless subsystem
method of quantum information science used to protect quantum states against
undesired noise. The relational theory naturally predicts a fundamental
decoherence mechanism, so an arrow of time emerges from a time-symmetric
theory. Moreover, there is no need for a "collapse of the wave packet" in our
model: the probability interpretation is only applied to diagonal density
operators. Finally, the physical states of the relational theory can be
described in terms of "spin networks" introduced by Penrose as a combinatorial
description of geometry, and widely studied in the loop formulation of quantum
gravity. Thus, our simple bottom-up approach (starting from the semi-classical
limit to derive the fully relational quantum theory) may offer interesting
insights on the low energy limit of quantum gravity.Comment: References added, extended discussio
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