201 research outputs found
Stationary measure for two-state space-inhomogeneous quantum walk in one dimension
We consider the two-state space-inhomogeneous coined quantum walk (QW) in one
dimension. For a general setting, we obtain the stationary measure of the QW by
solving the eigenvalue problem. As a corollary, stationary measures of the
multi-defect model and space-homogeneous QW are derived. The former is a
generalization of the previous works on one-defect model and the latter is a
generalization of the result given by Konno and Takei (2015).Comment: 15 pages, revised version, Yokohama Mathematical Journal (in press
The stationary measure for diagonal quantum walk with one defect
This study is motivated by the previous work [14]. We treat 3 types of the
one-dimensional quantum walks (QWs), whose time evolutions are described by
diagonal unitary matrix, and diagonal unitary matrices with one defect. In this
paper, we call the QW defined by diagonal unitary matrices, "the diagonal QW",
and we consider the stationary distributions of generally 2-state diagonal QW
with one defect, 3-state space-homogeneous diagonal QW, and 3-state diagonal QW
with one defect. One of the purposes of our study is to characterize the QWs by
the stationary measure, which may lead to answer the basic and natural
question, "What the stationary measure is for one-dimensional QWs ?". In order
to analyze the stationary distribution, we focus on the corresponding
eigenvalue problems and the definition of the stationary measure.Comment: 10 page
ã«ã³ãµã€ ãã€ãã·ã±ã³ ã ãã· ãã㊠ãã³ã»ã ã¿ã«ã¯ãã ãã· ã³ãŠãŸãŠ ã ã·ãã³ ã«ã©
The flipped orbit of KELT-19Ab inferred from the symmetric TESS transit light curves
Dozens of planets are now discovered with large orbital obliquity, and have
become the proof for the dynamical evolution of planetary orbits. In the
current samples, there is an apparent clustering of planets around ,
and also an absence of planets around although the latter is
expected by some theories. Statistical extrapolation using Hierarchical
Bayesian Analysis have recently refuted the significant clustering around
and suggested that the distribution may actually be broader. In this
work, the symmetric TESS transit light curve of KELT-19Ab is analyzed using
gravity darkening to measure its true obliquity. Its large sky projected
obliquity makes KELT-19Ab
the only currently known planet with obliquity potentially close to
. We apply spectroscopic constraints on and
as well as theoretical constraints on the limb-darkening coefficients
to find that the KELT-19Ab's obliquity is , in favor of a flipped orbit. The result
is consistent with the statistically inferred uniformity of obliquity
distribution, and also highlights the applicability of the gravity darkening
technique to symmetric light curves.Comment: 12 pages, 6 figures. Accepted for publication in MNRA
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