2,665 research outputs found
Infinite matrices may violate the associative law
The momentum operator for a particle in a box is represented by an infinite
order Hermitian matrix . Its square is well defined (and diagonal),
but its cube is ill defined, because . Truncating these
matrices to a finite order restores the associative law, but leads to other
curious results.Comment: final version in J. Phys. A28 (1995) 1765-177
Coarse Graining Makes It Hard to See Micro-Macro Entanglement
Observing quantum effects such as superpositions and entanglement in
macroscopic systems requires not only a system that is well protected against
environmental decoherence, but also sufficient measurement precision. Motivated
by recent experiments, we study the effects of coarse-graining in photon number
measurements on the observability of micro-macro entanglement that is created
by greatly amplifying one photon from an entangled pair. We compare the results
obtained for a unitary quantum cloner, which generates micro-macro
entanglement, and for a measure-and-prepare cloner, which produces a separable
micro-macro state. We show that the distance between the probability
distributions of results for the two cloners approaches zero for a fixed
moderate amount of coarse-graining. Proving the presence of micro-macro
entanglement therefore becomes progressively harder as the system size
increases.Comment: 5 pages, 3 figure
The Edge of Quantum Chaos
We identify a border between regular and chaotic quantum dynamics. The border
is characterized by a power law decrease in the overlap between a state evolved
under chaotic dynamics and the same state evolved under a slightly perturbed
dynamics. For example, the overlap decay for the quantum kicked top is well
fitted with (with the nonextensive entropic
index and depending on perturbation strength) in the region
preceding the emergence of quantum interference effects. This region
corresponds to the edge of chaos for the classical map from which the quantum
chaotic dynamics is derived.Comment: 4 pages, 4 figures, revised version in press PR
Wigner's little group and Berry's phase for massless particles
The ``little group'' for massless particles (namely, the Lorentz
transformations that leave a null vector invariant) is isomorphic to
the Euclidean group E2: translations and rotations in a plane. We show how to
obtain explicitly the rotation angle of E2 as a function of and we
relate that angle to Berry's topological phase. Some particles admit both signs
of helicity, and it is then possible to define a reduced density matrix for
their polarization. However, that density matrix is physically meaningless,
because it has no transformation law under the Lorentz group, even under
ordinary rotations.Comment: 4 pages revte
Kochen-Specker theorem for a single qubit using positive operator-valued measures
A proof of the Kochen-Specker theorem for a single two-level system is
presented. It employs five eight-element positive operator-valued measures and
a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure
Influence of detector motion in entanglement measurements with photons
We investigate how the polarization correlations of entangled photons
described by wave packets are modified when measured by moving detectors. For
this purpose, we analyze the Clauser-Horne-Shimony-Holt Bell inequality as a
function of the apparatus velocity. Our analysis is motivated by future
experiments with entangled photons designed to use satellites. This is a first
step towards the implementation of quantum information protocols in a global
scale
Evolution of Liouville density of a chaotic system
An area-preserving map of the unit sphere, consisting of alternating twists
and turns, is mostly chaotic. A Liouville density on that sphere is specified
by means of its expansion into spherical harmonics. That expansion initially
necessitates only a finite number of basis functions. As the dynamical mapping
proceeds, it is found that the number of non-negligible coefficients increases
exponentially with the number of steps. This is to be contrasted with the
behavior of a Schr\"odinger wave function which requires, for the analogous
quantum system, a basis of fixed size.Comment: LaTeX 4 pages (27 kB) followed by four short PostScript files (2 kB +
2 kB + 1 kB + 4 kB
Non-Contextual Hidden Variables and Physical Measurements
For a hidden variable theory to be indistinguishable from quantum theory for
finite precision measurements, it is enough that its predictions agree for some
measurement within the range of precision. Meyer has recently pointed out that
the Kochen-Specker theorem, which demonstrates the impossibility of a
deterministic hidden variable description of ideal spin measurements on a spin
1 particle, can thus be effectively nullified if only finite precision
measurements are considered. We generalise this result: it is possible to
ascribe consistent outcomes to a dense subset of the set of projection valued
measurements, or to a dense subset of the set of positive operator valued
measurements, on any finite dimensional system. Hence no Kochen-Specker like
contradiction can rule out hidden variable theories indistinguishable from
quantum theory by finite precision measurements in either class.Comment: Typo corrected. Final version: to appear in Phys. Rev. Let
Optical doping and damage formation in AIN by Eu implantation
AlN films grown on sapphire were implanted with 300 keV Eu ions to fluences from 3×1014 to 1.4×1017 atoms/cm2 in two different geometries: “channeled” along the c-axis and “random” with a 10° angle between the ion beam and the surface normal. A detailed study of implantation damage accumulation is presented. Strong ion channeling effects are observed leading to significantly decreased damage levels for the channeled implantation within the entire fluence range. For random implantation, a buried amorphous layer is formed at the highest fluences. Red Eu-related photoluminescence at room temperature is observed in all samples with highest intensities for low damage samples (low fluence and channeled implantation) after annealing. Implantation damage, once formed, is shown to be stable up to very high temperatures.FCT - POCI/FIS/57550/2004FCT - PTDC/FIS/66262/2006FCT - PTDC/CTM/100756/200
Chaotic Evolution in Quantum Mechanics
A quantum system is described, whose wave function has a complexity which
increases exponentially with time. Namely, for any fixed orthonormal basis, the
number of components required for an accurate representation of the wave
function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure
- …