43,948 research outputs found
Doubled Conformal Compactification
We use Weyl transformations between the Minkowski spacetime and dS/AdS
spacetime to show that one cannot well define the electrodynamics globally on
the ordinary conformal compactification of the Minkowski spacetime (or dS/AdS
spacetime), where the electromagnetic field has a sign factor (and thus is
discountinuous) at the light cone. This problem is intuitively and clearly
shown by the Penrose diagrams, from which one may find the remedy without too
much difficulty. We use the Minkowski and dS spacetimes together to cover the
compactified space, which in fact leads to the doubled conformal
compactification. On this doubled conformal compactification, we obtain the
globally well-defined electrodynamics.Comment: 14 pages, 4 figure
Bell-CHSH function approach to quantum phase transitions in matrix product systems
Recently, nonlocality and Bell inequalities have been used to investigate
quantum phase transitions (QPTs) in low-dimensional quantum systems.
Nonlocality can be detected by the Bell-CHSH function (BCF). In this work, we
extend the study of BCF to the QPTs in matrix product systems (MPSs). In this
kind of QPTs, the ground-state energy keeps analytical in the vicinity of the
QPT points, and is usually called the MPS-QPTs. For several typical models, our
results show that BCF can signal the MPS-QPTs very well. In addition, we find
BCF can capture signal of QPTs in unentangled states and classical states, for
which other measures of quantum correlation (quantum entanglement and quantum
discord) fail. Furthermore, we find that in these MPSs, there exists some kind
of quantum correlation which cannot be characterized by entanglement, or by
nonlocality.Comment: 12 pages, 4 figure
The Quasi-normal Modes of Charged Scalar Fields in Kerr-Newman black hole and Its Geometric Interpretation
It is well-known that there is a geometric correspondence between
high-frequency quasi-normal modes (QNMs) and null geodesics (spherical photon
orbits). In this paper, we generalize such correspondence to charged scalar
field in Kerr-Newman space-time. In our case, the particle and black hole are
all charged, so one should consider non-geodesic orbits. Using the WKB
approximation, we find that the real part of quasi-normal frequency corresponds
to the orbits frequency, the imaginary part of the frequency corresponds to the
Lyapunov exponent of these orbits and the eigenvalue of angular equation
corresponds to carter constant. From the properties of the imaginary part of
quasi-normal frequency of charged massless scalar field, we can still find that
the QNMs of charged massless scalar field possess the zero damping modes in
extreme Kerr-Newman spacetime under certain condition which has been fixed in
this paper.Comment: 30 pages, many figures, to appear in JHE
Multi-view Regularized Gaussian Processes
Gaussian processes (GPs) have been proven to be powerful tools in various
areas of machine learning. However, there are very few applications of GPs in
the scenario of multi-view learning. In this paper, we present a new GP model
for multi-view learning. Unlike existing methods, it combines multiple views by
regularizing marginal likelihood with the consistency among the posterior
distributions of latent functions from different views. Moreover, we give a
general point selection scheme for multi-view learning and improve the proposed
model by this criterion. Experimental results on multiple real world data sets
have verified the effectiveness of the proposed model and witnessed the
performance improvement through employing this novel point selection scheme
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