1,000 research outputs found
Spatial Degrees of Freedom in Everett Quantum Mechanics
Stapp claims that, when spatial degrees of freedom are taken into account,
Everett quantum mechanics is ambiguous due to a "core basis problem." To
examine an aspect of this claim I generalize the ideal measurement model to
include translational degrees of freedom for both the measured system and the
measuring apparatus. Analysis of this generalized model using the Everett
interpretation in the Heisenberg picture shows that it makes unambiguous
predictions for the possible results of measurements and their respective
probabilities. The presence of translational degrees of freedom for the
measuring apparatus affects the probabilities of measurement outcomes in the
same way that a mixed state for the measured system would. Examination of a
measurement scenario involving several observers illustrates the consistency of
the model with perceived spatial localization of the measuring apparatus.Comment: 34 pp., no figs. Introduction, discussion revised. Material
tangential to main point remove
Negative Energies in the Dirac equation
It is easy to check that both algebraic equation Det (hat p - m) =0 and Det
(hat p + m) =0 for u- and v- 4-spinors have solutions with p_0= pm E_p = pm
sqrt bf p^2 +m^2. The same is true for higher-spin equations. Meanwhile, every
book considers the equality p_0=E_p for both u- and v- spinors of the
(1/2,0)+(0,1/2)) representation only, thus applying the
Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy
solutions. The recent Ziino works (and, independently, the articles of several
others) show that the Fock space can be doubled. We re-consider this
possibility on the quantum field level for both s=1/2 and higher spin
particles.Comment: 8 pages, no figures. Accepted in Zeitschrift fur Naturforschun
Suppression of inhomogeneous broadening in rf spectroscopy of optically trapped atoms
We present a novel method for reducing the inhomogeneous frequency broadening
in the hyperfine splitting of the ground state of optically trapped atoms. This
reduction is achieved by the addition of a weak light field, spatially
mode-matched with the trapping field and whose frequency is tuned in-between
the two hyperfine levels. We experimentally demonstrate the new scheme with Rb
85 atoms, and report a 50-fold narrowing of the rf spectrum
On the Evolution Equation for Magnetic Geodesics
In this paper we prove the existence of long time solutions for the parabolic
equation for closed magnetic geodesics.Comment: In this paper we prove the existence of long time solutions for the
parabolic equation for closed magnetic geodesic
Role of Disorder on the Quantum Critical Point of a Model for Heavy Fermions
A zero temperature real space renormalization group (RG) approach is used to
investigate the role of disorder near the quantum critical point (QCP) of a
Kondo necklace (XY-KN) model. In the pure case this approach yields
implying that any coupling between the local moments and the
conduction electrons leads to a non-magnetic phase. We also consider an
anisotropic version of the model (), for which there is a quantum phase
transition at a finite value of the ratio between the coupling and the
bandwidth, . Disorder is introduced either in the on-site interactions
or in the hopping terms. We find that in both cases randomness is irrelevant in
the model, i.e., the disorder induced magnetic-non-magnetic quantum
phase transition is controlled by the same exponents of the pure case. Finally,
we show the fixed point distributions at the atractors of the
disordered, non-magnetic phases.Comment: 5 pages, 3 figure
Quantum mechanical analysis of the equilateral triangle billiard: periodic orbit theory and wave packet revivals
Using the fact that the energy eigenstates of the equilateral triangle
infinite well (or billiard) are available in closed form, we examine the
connections between the energy eigenvalue spectrum and the classical closed
paths in this geometry, using both periodic orbit theory and the short-term
semi-classical behavior of wave packets. We also discuss wave packet revivals
and show that there are exact revivals, for all wave packets, at times given by
where and are the length of one side
and the mass of the point particle respectively. We find additional cases of
exact revivals with shorter revival times for zero-momentum wave packets
initially located at special symmetry points inside the billiard. Finally, we
discuss simple variations on the equilateral
() triangle, such as the half equilateral
() triangle and other `foldings', which have
related energy spectra and revival structures.Comment: 34 pages, 9 embedded .eps figure
Superradiation from Crystals of High-Spin Molecular Nanomagnets
Phenomenological theory of superradiation from crystals of high-spin
molecules is suggested. We show that radiation friction can cause a
superradiation pulse and investigate the role of magnetic anisotropy, external
magnetic field and dipole-dipole interactions. Depending on the contribution of
all these factors at low temperature, several regimes of magnetization of
crystal sample are described. Very fast switch of magnetization's direction for
some sets of parameters is predicted.Comment: 10 pages, 3 figure
Slowly Rotating General Relativistic Superfluid Neutron Stars with Relativistic Entrainment
Neutron stars that are cold enough should have two or more
superfluids/supercondutors in their inner crusts and cores. The implication of
superfluidity/superconductivity for equilibrium and dynamical neutron star
states is that each individual particle species that forms a condensate must
have its own, independent number density current and equation of motion that
determines that current. An important consequence of the quasiparticle nature
of each condensate is the so-called entrainment effect, i.e. the momentum of a
condensate is a linear combination of its own current and those of the other
condensates. We present here the first fully relativistic modelling of slowly
rotating superfluid neutron stars with entrainment that is accurate to the
second-order in the rotation rates. The stars consist of superfluid neutrons,
superconducting protons, and a highly degenerate, relativistic gas of
electrons. We use a relativistic - mean field model for the
equation of state of the matter and the entrainment. We determine the effect of
a relative rotation between the neutrons and protons on a star's total mass,
shape, and Kepler, mass-shedding limit.Comment: 30 pages, 10 figures, uses ReVTeX
Robust high-dimensional precision matrix estimation
The dependency structure of multivariate data can be analyzed using the
covariance matrix . In many fields the precision matrix
is even more informative. As the sample covariance estimator is singular in
high-dimensions, it cannot be used to obtain a precision matrix estimator. A
popular high-dimensional estimator is the graphical lasso, but it lacks
robustness. We consider the high-dimensional independent contamination model.
Here, even a small percentage of contaminated cells in the data matrix may lead
to a high percentage of contaminated rows. Downweighting entire observations,
which is done by traditional robust procedures, would then results in a loss of
information. In this paper, we formally prove that replacing the sample
covariance matrix in the graphical lasso with an elementwise robust covariance
matrix leads to an elementwise robust, sparse precision matrix estimator
computable in high-dimensions. Examples of such elementwise robust covariance
estimators are given. The final precision matrix estimator is positive
definite, has a high breakdown point under elementwise contamination and can be
computed fast
BCI-Based Navigation in Virtual and Real Environments
A Brain-Computer Interface (BCI) is a system that enables people to control an external device with their brain activity, without the need of any muscular activity. Researchers in the BCI field aim to develop applications to improve the quality of life of severely disabled patients, for whom a BCI can be a useful channel for interaction with their environment. Some of these systems are intended to control a mobile device (e. g. a wheelchair). Virtual Reality is a powerful tool that can provide the subjects with an opportunity to train and to test different applications in a safe environment. This technical review will focus on systems aimed at navigation, both in virtual and real environments.This work was partially supported by the Innovation, Science and Enterprise Council of the Junta de AndalucĂa (Spain), project P07-TIC-03310, the Spanish Ministry of Science and Innovation, project TEC 2011-26395 and by the European fund ERDF
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