13,402 research outputs found
Entanglement in holographic dark energy models
We study a process of equilibration of holographic dark energy (HDE) with the
cosmic horizon around the dark-energy dominated epoch. This process is
characterized by a huge amount of information conveyed across the horizon,
filling thereby a large gap in entropy between the system on the brink of
experiencing a sudden collapse to a black hole and the black hole itself. At
the same time, even in the absence of interaction between dark matter and dark
energy, such a process marks a strong jump in the entanglement entropy,
measuring the quantum-mechanical correlations between the horizon and its
interior. Although the effective quantum field theory (QFT) with a peculiar
relationship between the UV and IR cutoffs, a framework underlying all HDE
models, may formally account for such a huge shift in the number of distinct
quantum states, we show that the scope of such a framework becomes tremendously
restricted, devoiding it virtually any application in other cosmological epochs
or particle-physics phenomena. The problem of negative entropies for the
non-phantom stuff is also discussed.Comment: 10 pages, version to appear in PL
Effective field theory, large number of particle species, and holography
An effective quantum field theory (QFT) with a manifest UV/IR connection, so
as to be valid for arbitrarily large volumes, can successfully be applied to
the cosmological dark energy problem as well as the cosmological constant (CC)
problem. Motivated by recent approaches to the hierarchy problem, we develop
such a framework with a large number of particle species. When applying to
systems on the brink of experiencing a sudden collapse to a black hole, we find
that the entropy, unlike the total energy, now becomes an increasing function
of the number of field species. An internal consistency of the theory is then
used to infer the upper bound on the number of particle species, showing
consistency with the holographic Bekenstein-Hawking bound. This may thus serve
to fill in a large gap in entropy of any non-black hole configuration of matter
and the black holes. In addition, when the bound is saturated the entanglement
entropy matches the black hole entropy, thus solving the multiplicity of
species problem. In a cosmological setting, the maximum allowable number of
species becomes a function of cosmological time, reaching its minimal value in
a low-entropy post-reheating epoch.Comment: 8 pages, minor corrections, a reference added, to appear in PL
The topological biquandle of a link
To every oriented link , we associate a topologically defined biquandle
, which we call the topological biquandle of .
The construction of is similar to the topological
description of the fundamental quandle given by Matveev. We find a presentation
of the topological biquandle and explain how it is related to the fundamental
biquandle of the link.Comment: 14 pages, 12 figure
Constructing biquandles
We define biquandle structures on a given quandle, and show that any
biquandle is given by some biquandle structure on its underlying quandle. By
determining when two biquandle structures yield isomorphic biquandles, we
obtain a relationship between the automorphism group of a biquandle and the
automorphism group of its underlying quandle. As an application, we determine
the automorphism groups of Alexander and dihedral biquandles. We also discuss
product biquandles and describe their automorphism groups.Comment: 17 page
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