22,235 research outputs found
Numerical studies of planar closed random walks
Lattice numerical simulations for planar closed random walks and their
winding sectors are presented. The frontiers of the random walks and of their
winding sectors have a Hausdorff dimension . However, when properly
defined by taking into account the inner 0-winding sectors, the frontiers of
the random walks have a Hausdorff dimension .Comment: 15 pages, 15 figure
Universal joint-measurement uncertainty relation for error bars
We formulate and prove a new, universally valid uncertainty relation for the necessary error bar widths in any approximate joint measurement of position and momentum
Large U_{e3} and Tri-bimaximal Mixing
We investigate in a model-independent way to what extent one can perturb
tri-bimaximal mixing in order to generate a sizable value of |U_{e3}|, while at
the same time keeping solar neutrino mixing near its measured value, which is
close to sin^2 theta_{12} = 1/3. Three straightforward breaking mechanisms to
generate |U_{e3}| of about 0.1 are considered. For charged lepton corrections,
the suppression of a sizable contribution to sin^2 theta_{12} can be achieved
if CP violation in neutrino oscillations is almost maximal. Generation of the
indicated value of |U_{e3}| of about 0.1 through renormalization group
corrections requires the neutrinos to be quasi-degenerate in mass. The
consistency with the allowed range of sin^2 theta_{12} together with large
running of |U_{e3}| forces one of the Majorana phases to be close to pi. This
implies large cancellations in the effective Majorana mass governing
neutrino-less double beta, constraining it to lie near its minimum allowed
value of m_0 cos 2 theta_{12}, where m_0 is greater than about 0.1 eV. Finally,
explicit breaking of the neutrino mass matrix in the inverted hierarchical and
quasi-degenerate neutrino mass spectrum cases is similarly correlated with the
effective Majorana mass, although to a lesser extent. The implied values for
the atmospheric neutrino mixing angle theta_{23} are given in all cases.Comment: 20 pages, 9 figure
Observation of Scalar Aharonov-Bohm Effect with Longitudinally Polarized Neutrons
We have carried out a neutron interferometry experiment using longitudinally polarized neutrons to observe the scalar Aharonov-Bohm effect. The neutrons inside the interferometer are polarized parallel to an applied pulsed magnetic field B(t). The pulsed B field is spatially uniform so it exerts no force on the neutrons. Its direction also precludes the presence of any classical torque to change the neutron polarization
Scalar Aharonov-Bohm effect with longitudinally polarized neutrons
In the scalar Aharonov-Bohm effect, a charged particle (electron) interacts with the scalar electrostatic potential U in the field-free (i.e., force-free) region inside an electrostatic cylinder (Faraday cage). Using a perfect single-crystal neutron interferometer we have performed a âdualâ scalar Aharonov-Bohm experiment by subjecting polarized thermal neutrons to a pulsed magnetic field. The pulsed magnetic field was spatially uniform, precluding any force on the neutrons. Aligning the direction of the pulsed magnetic field to the neutron magnetic moment also rules out any classical torque acting to change the neutron polarization. The observed phase shift is purely quantum mechanical in origin. A detailed description of the experiment, performed at the University of Missouri Research Reactor, and its interpretation is given in this paper
On Infinite Quon Statistics and "Ambiguous" Statistics
We critically examine a recent suggestion that "ambiguous" statistics is
equivalent to infinite quon statistics and that it describes a dilute,
nonrelativistics ideal gas of extremal black holes. We show that these two
types of statistics are different and that the description of extremal black
holes in terms of "ambiguous" statistics cannot be applied.Comment: Latex, 9 pages, no figures, to appear in Mod.Phys.Lett.
Exact Energy-Time Uncertainty Relation for Arrival Time by Absorption
We prove an uncertainty relation for energy and arrival time, where the
arrival of a particle at a detector is modeled by an absorbing term added to
the Hamiltonian. In this well-known scheme the probability for the particle's
arrival at the counter is identified with the loss of normalization for an
initial wave packet. Under the sole assumption that the absorbing term vanishes
on the initial wave function, we show that and , where denotes the mean
arrival time, and is the probability for the particle to be eventually
absorbed. Nearly minimal uncertainty can be achieved in a two-level system, and
we propose a trapped ion experiment to realize this situation.Comment: 8 pages, 2 figure
Maximal violation of the I3322 inequality using infinite dimensional quantum systems
The I3322 inequality is the simplest bipartite two-outcome Bell inequality
beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three
two-outcome measurements per party. In case of the CHSH inequality the maximal
quantum violation can already be attained with local two-dimensional quantum
systems, however, there is no such evidence for the I3322 inequality. In this
paper a family of measurement operators and states is given which enables us to
attain the largest possible quantum value in an infinite dimensional Hilbert
space. Further, it is conjectured that our construction is optimal in the sense
that measuring finite dimensional quantum systems is not enough to achieve the
true quantum maximum. We also describe an efficient iterative algorithm for
computing quantum maximum of an arbitrary two-outcome Bell inequality in any
given Hilbert space dimension. This algorithm played a key role to obtain our
results for the I3322 inequality, and we also applied it to improve on our
previous results concerning the maximum quantum violation of several bipartite
two-outcome Bell inequalities with up to five settings per party.Comment: 9 pages, 3 figures, 1 tabl
The structure of classical extensions of quantum probability theory
On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called MisraâBugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed
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