1,042 research outputs found
Incomplete Transition Complexity of Basic Operations on Finite Languages
The state complexity of basic operations on finite languages (considering
complete DFAs) has been in studied the literature. In this paper we study the
incomplete (deterministic) state and transition complexity on finite languages
of boolean operations, concatenation, star, and reversal. For all operations we
give tight upper bounds for both description measures. We correct the published
state complexity of concatenation for complete DFAs and provide a tight upper
bound for the case when the right automaton is larger than the left one. For
all binary operations the tightness is proved using family languages with a
variable alphabet size. In general the operational complexities depend not only
on the complexities of the operands but also on other refined measures.Comment: 13 page
Entropic force and its cosmological implications
We investigate a possibility of realizing the entropic force into the
cosmology. A main issue is how the holographic screen is implemented in the
Newtonian cosmology. Contrary to the relativistic realization of Friedmann
equations, we do not clarify the connection between Newtonian cosmology and
entropic force because there is no way of implementing the holographic screen
in the Newtonian cosmology.Comment: 16 pages, no figures, version "Accepted for publication in
Astrophysics & Space Science
Does entropic force always imply the Newtonian force law?
We study the entropic force by introducing a bound between
entropy and area which was derived by imposing the non-gravitational collapse
condition. In this case, applying a modified entropic force to this system does
not lead to the Newtonian force law.Comment: 11 pages, version to appear in EPJ
Caustic avoidance in Horava-Lifshitz gravity
There are at least four versions of Horava-Lishitz gravity in the literature.
We consider the version without the detailed balance condition with the
projectability condition and address one aspect of the theory: avoidance of
caustics for constant time hypersurfaces. We show that there is no caustic with
plane symmetry in the absence of matter source if \lambda\ne 1. If \lambda=1 is
a stable IR fixed point of the renormalization group flow then \lambda is
expected to deviate from 1 near would-be caustics, where the extrinsic
curvature increases and high-energy corrections become important. Therefore,
the absence of caustics with \lambda\ne 1 implies that caustics cannot form
with this symmetry in the absence of matter source. We argue that inclusion of
matter source will not change the conclusion. We also argue that caustics with
codimension higher than one will not form because of repulsive gravity
generated by nonlinear higher curvature terms. These arguments support our
conjecture that there is no caustic for constant time hypersurfaces. Finally,
we discuss implications to the recently proposed scenario of ``dark matter as
integration constant''.Comment: 19 pages; extended to general z \geq 3, typos corrected (v2); version
accepted for publication in JCAP (v3
The Black Hole and Cosmological Solutions in IR modified Horava Gravity
Recently Horava proposed a renormalizable gravity theory in four dimensions
which reduces to Einstein gravity with a non-vanishing cosmological constant in
IR but with improved UV behaviors. Here, I study an IR modification which
breaks "softly" the detailed balance condition in Horava model and allows the
asymptotically flat limit as well. I obtain the black hole and cosmological
solutions for "arbitrary" cosmological constant that represent the analogs of
the standard Schwartzschild-(A)dS solutions which can be asymptotically (A)dS
as well as flat and I discuss some thermodynamical properties. I also obtain
solutions for FRW metric with an arbitrary cosmological constant. I study its
implication to the dark energy and find that it seems to be consistent with
current observational data.Comment: Footnote 5 about the the very meaning of the horizons and Hawking
temperature is added; Accepted in JHE
Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
This research was supported by the Australian Research Council, the ImPACT Program of the Council for Science, Technology and Innovation (Cabinet Office, Government of Japan), the RIKEN iTHES Project, the MURI Center for Dynamic Magneto-Optics, a Grant-in-Aid for Scientific Research (type A), and the State of Bavaria.Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as for fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (that is, non-Hermitian) quantum system, which requires constant pumping of energy and continuously decays, releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and loss. However, the inherent non-Hermitian nature of this potential has so far been largely ignored in exciton-polariton physics. Here we demonstrate that non-Hermiticity dramatically modifies the structure of modes and spectral degeneracies in exciton-polariton systems, and, therefore, will affect their quantum transport, localization and dynamical properties. Using a spatially structured optical pump, we create a chaotic exciton-polariton billiard-a two-dimensional area enclosed by a curved potential barrier. Eigenmodes of this billiard exhibit multiple non-Hermitian spectral degeneracies, known as exceptional points. Such points can cause remarkable wave phenomena, such as unidirectional transport, anomalous lasing/absorption and chiral modes. By varying parameters of the billiard, we observe crossing and anti-crossing of energy levels and reveal the non-trivial topological modal structure exclusive to non-Hermitian systems. We also observe mode switching and a topological Berry phase for a parameter loop encircling the exceptional point. Our findings pave the way to studies of non-Hermitian quantum dynamics of exciton-polaritons, which may uncover novel operating principles for polariton-based devices.PostprintPeer reviewe
Entropic Corrections to Coulomb's Law
Two well-known quantum corrections to the area law have been introduced in
the literatures, namely, logarithmic and power-law corrections. Logarithmic
corrections, arises from loop quantum gravity due to thermal equilibrium
fluctuations and quantum fluctuations, while, power-law correction appears in
dealing with the entanglement of quantum fields in and out the horizon.
Inspired by Verlinde's argument on the entropic force, and assuming the quantum
corrected relation for the entropy, we propose the entropic origin for the
Coulomb's law in this note. Also we investigate the Uehling potential as a
radiative correction to Coulomb potential in 1-loop order and show that for
some value of distance the entropic corrections of the Coulomb's law is
compatible with the vacuum-polarization correction in QED. So, we derive
modified Coulomb's law as well as the entropy corrected Poisson's equation
which governing the evolution of the scalar potential . Our study further
supports the unification of gravity and electromagnetic interactions based on
the holographic principle.Comment: 17 pages, 5 figures, accepted in IJT
Horava-Lifshitz f(R) Gravity
This paper is devoted to the construction of new type of f(R) theories of
gravity that are based on the principle of detailed balance. We discuss two
versions of these theories with and without the projectability condition.Comment: 22 pages, references adde
New agegraphic dark energy in Horava-Lifshitz cosmology
We investigate the new agegraphic dark energy scenario in a universe governed
by Horava-Lifshitz gravity. We consider both the detailed and non-detailed
balanced version of the theory, we impose an arbitrary curvature, and we allow
for an interaction between the matter and dark energy sectors. Extracting the
differential equation for the evolution of the dark energy density parameter
and performing an expansion of the dark energy equation-of-state parameter, we
calculate its present and its low-redshift value as functions of the dark
energy and curvature density parameters at present, of the Horava-Lifshitz
running parameter , of the new agegraphic dark energy parameter ,
and of the interaction coupling . We find that
and . Although this analysis indicates that the
scenario can be compatible with observations, it does not enlighten the
discussion about the possible conceptual and theoretical problems of
Horava-Lifshitz gravity.Comment: 17 pages, no figures, version published at JCA
Observational constraints on Horava-Lifshitz cosmology
We use observational data from Type Ia Supernovae (SNIa), Baryon Acoustic
Oscillations (BAO), and Cosmic Microwave Background (CMB), along with
requirements of Big Bang Nucleosynthesis (BBN), to constrain the cosmological
scenarios governed by Horava-Lifshitz gravity. We consider both the detailed
and non-detailed balance versions of the gravitational sector, and we include
the matter and radiation sectors. We conclude that the detailed-balance
scenario cannot be ruled out from the observational point of view, however the
corresponding likelihood contours impose tight constraints on the involved
parameters. The scenario beyond detailed balance is compatible with
observational data, and we present the corresponding stringent constraints and
contour-plots of the parameters. Although this analysis indicates that
Horava-Lifshitz cosmology can be compatible with observations, it does not
enlighten the discussion about its possible conceptual and theoretical
problems.Comment: 11 pages, 6 figures, version published in JCA
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