25 research outputs found
A Universal Magnification Theorem III. Caustics Beyond Codimension Five
In the final paper of this series, we extend our results on magnification
invariants to the infinite family of A, D, E caustic singularities. We prove
that for families of general mappings between planes exhibiting any caustic
singularity of the A, D, E family, and for a point in the target space lying
anywhere in the region giving rise to the maximum number of lensed images (real
pre-images), the total signed magnification of the lensed images will always
sum to zero. The proof is algebraic in nature and relies on the Euler trace
formula.Comment: 8 page
On the Observables Describing a Quantum Reference Frame
A reference frame F is described by the element g of the Poincare' group P
which connects F with a given fixed frame F_0. If F is a quantum frame, defined
by a physical object following the laws of quantum physics, the parameters of g
have to be considered as quantum observables. However, these observables are
not compatible and some of them, namely the coordinates of the origin of F,
cannot be represented by self-adjoint operators. Both these difficulties can be
overcome by considering a positive-operator-valued measure (POVM) on P,
covariant with respect to the left translations of the group, namely a
covariance system. We develop a construction procedure for this kind of
mathematical structure. The formalism is also used to discuss the quantum
observables measured with respect to a quantum reference frame.Comment: 23 pages, no figure
Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates
We investigate a Bose-Einstein condensate with additional long-range dipolar
interaction in a cylindrically symmetric trap within a variational framework.
Compared to the ground state of this system, little attention has as yet been
payed to its unstable excited states. For thermal excitations, however, the
latter is of great interest, because it forms the "activated complex" that
mediates the collapse of the condensate. For a certain value of the s-wave
scatting length our investigations reveal a bifurcation in the transition
state, leading to the emergence of two additional and symmetry-breaking excited
states. Because these are of lower energy than their symmetric counterpart, we
predict the occurrence of a symmetry-breaking thermally induced collapse of
dipolar condensates. We show that its occurrence crucially depends on the trap
geometry and calculate the thermal decay rates of the system within leading
order transition state theory with the help of a uniform rate formula near the
rank-2 saddle which allows to smoothly pass the bifurcation.Comment: 6 pages, 3 figure
Position and momentum observables on R and on R^3
We characterize all position and momentum observables on R and on R^3. We
study some of their operational properties and discuss their covariant joint
observables.Comment: 18 page
Free energy of the Fr\"ohlich polaron in two and three dimensions
We present a novel Path Integral Monte Carlo scheme to solve the Fr\"ohlich
polaron model. At intermediate and strong electron-phonon coupling, the polaron
self-trapping is properly taken into account at the level of an effective
action obtained by a preaveraging procedure with a retarded trial action. We
compute the free energy at several couplings and temperatures in three and two
dimensions. Our results show that the accuracy of the Feynman variational upper
bound for the free energy is always better than 5% although the thermodynamics
derived from it is not correct. Our estimates of the ground state energies
demonstrate that the second cumulant correction to the variational upper bound
predicts the self energy to better than 1% at intermediate and strong coupling.Comment: RevTeX 7 pages 3 figures, revised versio
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
Semiclassical ionization dynamics of the hydrogen molecular ion in an electric field of arbitrary orientation
Quasi-static models of barrier suppression have played a major role in our
understanding of the ionization of atoms and molecules in strong laser fields.
Despite their success, in the case of diatomic molecules these studies have so
far been restricted to fields aligned with the molecular axis. In this paper we
investigate the locations and heights of the potential barriers in the hydrogen
molecular ion in an electric field of arbitrary orientation. We find that the
barriers undergo bifurcations as the external field strength and direction are
varied. This phenomenon represents an unexpected level of intricacy even on
this most elementary level of the dynamics. We describe the dynamics of
tunnelling ionization through the barriers semiclassically and use our results
to shed new light on the success of a recent theory of molecular tunnelling
ionization as well as earlier theories that restrict the electric field to be
aligned with the molecular axis
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
Projection Postulate and Atomic Quantum Zeno Effect
The projection postulate has been used to predict a slow-down of the time
evolution of the state of a system under rapidly repeated measurements, and
ultimately a freezing of the state. To test this so-called quantum Zeno effect
an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295 (1990)) in
which an atomic-level measurement was realized by means of a short laser pulse.
The relevance of the results has given rise to controversies in the literature.
In particular the projection postulate and its applicability in this experiment
have been cast into doubt. In this paper we show analytically that for a wide
range of parameters such a short laser pulse acts as an effective level
measurement to which the usual projection postulate applies with high accuracy.
The corrections to the ideal reductions and their accumulation over n pulses
are calculated. Our conclusion is that the projection postulate is an excellent
pragmatic tool for a quick and simple understanding of the slow-down of time
evolution in experiments of this type. However, corrections have to be
included, and an actual freezing does not seem possible because of the finite
duration of measurements.Comment: 25 pages, LaTeX, no figures; to appear in Phys. Rev.