56,563 research outputs found
Complexity and phase transitions in a holographic QCD model
Applying the "Complexity=Action" conjecture, we study the holographic
complexity close to crossover/phase transition in a holographic QCD model
proposed by Gubser et al. This model can realize three types of phase
transition, crossover or first and second order, depending on the parameters of
the dilaton potential. The re-scaled late-time growth rate of holographic
complexity density for the three cases is calculated. Our results show that it
experiences a fast drop/jump close to the critical point while approaching
constants far beyond the critical temperature. Moreover, close to the critical
temperature, it shows a behavior characterizing the type of the transition.
These features suggest that the growth rate of the holographic complexity may
be used as a good parameter to characterize the phase transition. The Lloyd's
bound is always satisfied for the cases we considered but only saturated for
the conformal case.Comment: v1: 14 pages, 2 figures; v2: refs added, minor modifications. arXiv
admin note: substantial text overlap with arXiv:1608.03072; v3: More details
on the Lloyd's bound, matching the published versio
Holographic entanglement entropy close to crossover/phase transition in strongly coupled systems
We investigate the behavior of entanglement entropy in the holographic QCD
model proposed by Gubser et al. By choosing suitable parameters of the scalar
self-interaction potential, this model can exhibit various types of phase
structures: crossover, first order and second order phase transitions. We use
entanglement entropy to probe the crossover/phase transition, and find that it
drops quickly/suddenly when the temperature approaches the critical point which
can be seen as a signal of confinement. Moreover, the critical behavior of the
entanglement entropy suggests that we may use it to characterize the
corresponding phase structures.Comment: v1:19 pages, 5 figures; v2: refs added; v3: 20 pages,
high-temperature behaviors of holographic entanglement entropy are given,
accecpted for publication by NP
A simple iterative algorithm for maxcut
We propose a simple iterative (SI) algorithm for the maxcut problem through
fully using an equivalent continuous formulation. It does not need rounding at
all and has advantages that all subproblems have explicit analytic solutions,
the cut values are monotonically updated and the iteration points converge to a
local optima in finite steps via an appropriate subgradient selection.
Numerical experiments on G-set demonstrate the performance. In particular, the
ratios between the best cut values achieved by SI and the best known ones are
at least and can be further improved to at least by a
preliminary attempt to break out of local optima.Comment: 30 pages, 1 figure. Subgradient selection, cost analysis and local
breakout are adde
A Bayesian Framework to Constrain the Photon Mass with a Catalog of Fast Radio Bursts
A hypothetical photon mass, , gives an energy-dependent light speed
in a Lorentz-invariant theory. Such a modification causes an additional time
delay between photons of different energies when they travel through a fixed
distance. Fast radio bursts (FRBs), with their short time duration and
cosmological propagation distance, are excellent astrophysical objects to
constrain . Here for the first time we develop a Bayesian framework
to study this problem with a catalog of FRBs. Those FRBs with and without
redshift measurement are both useful in this framework, and can be combined in
a Bayesian way. A catalog of 21 FRBs (including 20 FRBs without redshift
measurement, and one, FRB 121102, with a measured redshift ) give a combined limit ,
or equivalently (, or equivalently ) at 68% (95%) confidence level, which represents the
best limit that comes purely from kinematics. The framework proposed here will
be valuable when FRBs are observed daily in the future. Increment in the number
of FRBs, and refinement in the knowledge about the electron distributions in
the Milky Way, the host galaxies of FRBs, and the intergalactic median, will
further tighten the constraint.Comment: 10 pages, 6 figures; Physical Review D, in pres
On the Coverage Bound Problem of Empirical Likelihood Methods For Time Series
The upper bounds on the coverage probabilities of the confidence regions
based on blockwise empirical likelihood [Kitamura (1997)] and nonstandard
expansive empirical likelihood [Nordman et al. (2013)] methods for time series
data are investigated via studying the probability for the violation of the
convex hull constraint. The large sample bounds are derived on the basis of the
pivotal limit of the blockwise empirical log-likelihood ratio obtained under
the fixed-b asymptotics, which has been recently shown to provide a more
accurate approximation to the finite sample distribution than the conventional
chi-square approximation. Our theoretical and numerical findings suggest that
both the finite sample and large sample upper bounds for coverage probabilities
are strictly less than one and the blockwise empirical likelihood confidence
region can exhibit serious undercoverage when (i) the dimension of moment
conditions is moderate or large; (ii) the time series dependence is positively
strong; or (iii) the block size is large relative to sample size. A similar
finite sample coverage problem occurs for the nonstandard expansive empirical
likelihood. To alleviate the coverage bound problem, we propose to penalize
both empirical likelihood methods by relaxing the convex hull constraint.
Numerical simulations and data illustration demonstrate the effectiveness of
our proposed remedies in terms of delivering confidence sets with more accurate
coverage
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