Quantum walks and orbital states of a Weyl particle

The time-evolution equation of a one-dimensional quantum walker is exactly mapped to the three-dimensional Weyl equation for a zero-mass particle with spin 1/2, in which each wave number k of walker's wave function is mapped to a point \vec{q}(k) in the three-dimensional momentum space and \vec{q}(k) makes a planar orbit as k changes its value in [-\pi, \pi). The integration over k providing the real-space wave function for a quantum walker corresponds to considering an orbital state of a Weyl particle, which is defined as a superposition (curvilinear integration) of the energy-momentum eigenstates of a free Weyl equation along the orbit. Konno's novel distribution function of quantum-walker's pseudo-velocities in the long-time limit is fully controlled by the shape of the orbit and how the orbit is embedded in the three-dimensional momentum space. The family of orbital states can be regarded as a geometrical representation of the unitary group U(2) and the present study will propose a new group-theoretical point of view for quantum-walk problems.Comment: REVTeX4, 9 pages, 1 figure, v2: Minor corrections made for publication in Phys.Rev.

Wigner formula of rotation matrices and quantum walks

Quantization of a random-walk model is performed by giving a qudit (a multi-component wave function) to a walker at site and by introducing a quantum coin, which is a matrix representation of a unitary transformation. In quantum walks, the qudit of walker is mixed according to the quantum coin at each time step, when the walker hops to other sites. As special cases of the quantum walks driven by high-dimensional quantum coins generally studied by Brun, Carteret, and Ambainis, we study the models obtained by choosing rotation as the unitary transformation, whose matrix representations determine quantum coins. We show that Wigner's $(2j+1)$-dimensional unitary representations of rotations with half-integers $j$'s are useful to analyze the probability laws of quantum walks. For any value of half-integer $j$, convergence of all moments of walker's pseudovelocity in the long-time limit is proved. It is generally shown for the present models that, if $(2j+1)$ is even, the probability measure of limit distribution is given by a superposition of $(2j+1)/2$ terms of scaled Konno's density functions, and if $(2j+1)$ is odd, it is a superposition of $j$ terms of scaled Konno's density functions and a Dirac's delta function at the origin. For the two-, three-, and four-component models, the probability densities of limit distributions are explicitly calculated and their dependence on the parameters of quantum coins and on the initial qudit of walker is completely determined. Comparison with computer simulation results is also shown.Comment: v2: REVTeX4, 15 pages, 4 figure

Limit distributions of two-dimensional quantum walks

One-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t \to \infty$ of all joint moments of two components of walker's pseudovelocity, $X_t/t$ and $Y_t/t$, is proved and the probability density of limit distribution is derived. Dependence of the two-dimensional limit density function on the parameter of quantum coin and initial four-component qudit of quantum walker is determined. Symmetry of limit distribution on a plane and localization around the origin are completely controlled. Comparison with numerical results of direct computer-simulations is also shown.Comment: v3: REVTeX4, 20 pages, 6 figures, minor corrections made for publicatio

絵本における「比喩的表現」 : 「大きさ」の比喩的表現を子どもはどうとらえているか

絵本には,比喩的な語彙の使用が多い。それは文学的な表現であるだけでなく,対象者である幼児の内容理解を促進するために用いる場合もある。その際,対象者であるこどもの認識,知識,語彙にあわせた表現の配慮がなされる。絵本を作る側にいる者として,その比喩をどのような理解しているのかを,「ちいさなもの」「おおきなもの」を表現した絵本テキストを読み聞かせ,その大きさを幼児に行動で示させることで,比喩的表現の理解程度を検証した。Figurative speech is often used in children\u27s picture books. This is not merely a literary device but can also serve to facilitate understanding of the content for the intended audience of children readers. In suchcases, the child readers\u27 knowledge, experience and vocabulary must be carefully considered when selectingappropriate language. From the perspective of a creator of children\u27s picture books, a study was conducted to determine the ways in which children understand such figurative speech by reading them a text containingthe expressions "small things" and "large things", then having them act out their perceptions of size withtheir bodie

Altered Hemodynamics Associated with Pathogenesis of the Vertebral Artery Dissecting Aneurysms

The etiology of the vertebral dissecting aneurysms is largely unknown, and they frequently occurs in relatively healthy young men. Objectives and Methods. A series of 57 consecutive cases defined by angiography were evaluated with regard to deviation in the course of the affected and contralateral vertebral arteries. Division was into 3 types: Type I without any deviation, Type II with mild-to-moderate deviation but not over the midline; and Type III with marked deviation over to the contralateral side beyond the midline. Results. The most frequent type of VA running was Type III for the affected and Type I nonaffected side, with this being found in all 17 patients except one. All of the Type III dissections occurred just proximal to a tortuous portion, while in cases with Type-I- and Type-II-affected sides, the majority (33 of 39) occurred near the union of the vertebral artery. In 10 of 57, a non-dominant side was affected, all except one being of Type I or II. With 12 recent patients assessed angiographically in detail for hemodynamics, eleven patients showed contrast material retrograde inflowing into the pseudolumen from the distal portion of the dissection site. Turbulent blood flow was recognized in all of these patients with retrograde inflow. Conclusions. Turbulent blood flow is one etiology of vertebral artery dissection aneurysms, with the sites in the majority of the cases being just proximal to a tortuous portion or union of vessels. In cases with dissection proximal to the tortuous course of the vertebral artery, retrograde inflow will occur more frequently than antegrade, which should be taken into account in designing therapeutic strategies

Changes of Blood Flow Volume in the Superior Mesenteric Artery and Brachial Artery with Abdominal Thermal Stimulation

In traditional Chinese medicine, moxibustion is a local thermal therapy that is used for several conditions. Quantifying the effects of moxibustion therapy has been difficult because the treatment temperature depends on the physician's experience, and the temperature distribution in the target area is not uniform. This prospective observational study aims to quantify the effect of local thermal stimulation to the abdomen. We developed a heat transfer control device (HTCD) for local thermal stimulation. Twenty-four healthy subjects were enrolled and they underwent abdominal thermal stimulation to the para-umbilical region with the device for 20 min. Blood flow volume in the superior mesenteric artery (SMA) and brachial artery (BA), the heart rate and the blood pressure were measured at rest, 15 min after starting thermal stimulation and 10, 20, 30 and 40 min after completing thermal stimulation. Blood flow parameters were measured by high-resolution ultrasound. In the SMA, blood flow volume was significantly increased during thermal stimulation (P < .01), as well as at 10 min (P < .01) and 20 min (P < .05) after stimulation. In the BA, blood flow volume decreased at 40 min after stimulation (P < .01). In conclusion we could quantify the effect of local thermal stimulation with an HTCD and high-resolution ultrasound. Thermal stimulation of the para-umbilical region increased blood flow in the SMA 20 min after stimulation in healthy subjects