1,191 research outputs found
CMB statistical isotropy confirmation at all scales using multipole vectors
We present an efficient numerical code and conduct, for the first time, a
null and model-independent CMB test of statistical isotropy using Multipole
Vectors (MVs) at all scales. Because MVs are insensitive to the angular power
spectrum , our results are independent from the assumed cosmological
model. We avoid a posteriori choices and use pre-defined ranges of scales
, and in our analyses. We
find that all four masked Planck maps, from both 2015 and 2018 releases, are in
agreement with statistical isotropy for , . For
we detect anisotropies but this is indicative of simply the
anisotropy in the noise: there is no anisotropy for and an
increasing level of anisotropy at higher multipoles. Our findings of no
large-scale anisotropies seem to be a consequence of avoiding \emph{a
posteriori} statistics. We also find that the degree of anisotropy in the full
sky (i.e. unmasked) maps vary enormously (between less than 5 and over 1000
standard deviations) among the different mapmaking procedures and data
releases.Comment: v4: additional analysis which increased statistical sensitivity,
including new plots and tables; extended discussion; 15 pages, 14 figures, 7
tables. Matches published versio
Collective versus hub activation of epidemic phases on networks
We consider a general criterion to discern the nature of the threshold in
epidemic models on scale-free (SF) networks. Comparing the epidemic lifespan of
the nodes with largest degrees with the infection time between them, we propose
a general dual scenario, in which the epidemic transition is either ruled by a
hub activation process, leading to a null threshold in the thermodynamic limit,
or given by a collective activation process, corresponding to a standard phase
transition with a finite threshold. We validate the proposed criterion applying
it to different epidemic models, with waning immunity or heterogeneous
infection rates in both synthetic and real SF networks. In particular, a waning
immunity, irrespective of its strength, leads to collective activation with
finite threshold in scale-free networks with large exponent, at odds with
canonical theoretical approaches.Comment: Revised version accepted for publication in PR
Phase transitions with infinitely many absorbing states in complex networks
We instigate the properties of the threshold contact process (TCP), a process
showing an absorbing-state phase transition with infinitely many absorbing
states, on random complex networks. The finite size scaling exponents
characterizing the transition are obtained in a heterogeneous mean field (HMF)
approximation and compared with extensive simulations, particularly in the case
of heterogeneous scale-free networks. We observe that the TCP exhibits the same
critical properties as the contact process (CP), which undergoes an
absorbing-state phase transition to a single absorbing state. The accordance
among the critical exponents of different models and networks leads to
conjecture that the critical behavior of the contact process in a HMF theory is
a universal feature of absorbing state phase transitions in complex networks,
depending only on the locality of the interactions and independent of the
number of absorbing states. The conditions for the applicability of the
conjecture are discussed considering a parallel with the
susceptible-infected-susceptible epidemic spreading model, which in fact
belongs to a different universality class in complex networks.Comment: 9 pages, 6 figures to appear in Phys Rev
Schwarzschild-like black holes: Light-like trajectories and massless scalar absorption
Black holes are among the most intriguing objects in nature. They are
believed to be fully described by General Relativity (GR), and the
astrophysical black holes are expected to belong to the Kerr family, obeying
the no-hair theorems. Alternative theories of gravity or parameterized
deviations of GR allow black hole solutions, which have additional parameters
other than mass and angular momentum. We analyze a Schwarzschild-like metric,
proposed by Johannsen and Psaltis, characterized by its mass and a deformation
parameter. We compute the absorption cross section of massless scalar waves for
different values of this deformation parameter and compare it with the
corresponding scalar absorption cross section of the Schwarzschild black hole.
We also present analytical approximations for the absorption cross section in
the high-frequency regime. We check the consistence of our results comparing
the numerical and analytical approaches, finding excellent agreement.Comment: 8 pages, 14 figure
The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement
This paper considers the control landscape of quantum transitions in
multi-qubit systems driven by unitary transformations with single-qubit
interaction terms. The two-qubit case is fully analyzed to reveal the features
of the landscape including the nature of the absolute maximum and minimum, the
saddle points and the absence of traps. The results permit calculating the
Schmidt state starting from an arbitrary two-qubit state following the local
gradient flow. The analysis of multi-qubit systems is more challenging, but the
generalized Schmidt states may also be located by following the local gradient
flow. Finally, we show the relation between the generalized Schmidt states and
the entanglement measure based on the Bures distance
Treating some solid state problems with the Dirac equation
The ambiguity involved in the definition of effective-mass Hamiltonians for
nonrelativistic models is resolved using the Dirac equation. The multistep
approximation is extended for relativistic cases allowing the treatment of
arbitrary potential and effective-mass profiles without ordering problems. On
the other hand, if the Schrodinger equation is supposed to be used, our
relativistic approach demonstrate that both results are coincidents if the
BenDaniel and Duke prescription for the kinetic-energy operator is implemented.
Applications for semiconductor heterostructures are discussed.Comment: 06 pages, 5 figure
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