Coherent State Path Integral for Bloch Particle

We construct a coherent state path integral formalism for the one-dimensional Bloch particle within the single band model. The transition amplitude between two coherent states is a sum of transition amplitudes with different winding numbers on the two-dimensional phase space which has the same topology as that of the cylinder. Appearance of the winding number is due to the periodicity of the quasi-momentum of the Bloch particle. Our formalism is successfully applied to a semiclassical motion of the Bloch particle under a uniform electric field. The wave packet exhibits not only the Bloch oscillation but also a similar breathing to the one for the squeezed state of a harmonic oscillator.Comment: 10 pages, Revtev

Studies on erythropoiesis II. In vitro studies on red cell proliferation under varied oxygen tension

For the purpose to reveal the mechanism of the stimulated erythropoiesis in anemic condition, the author observed the numerical changes of the erythroblasts from normal rabbit bone marrow cultured under the environment of varied oxygen tensions, and revealed the following: 1. The erythroblasts incubated with air are increased after 24 to 48 hours and decreased gradually disappearing by 120 hours with a corresponding increase of erythrocytes. But no active proliferation of the stem cells or proerythroblasts is observed, all the cells have differentiated to erythrocytes. Hyperoxygen tension suppresses the increase of erythroblasts slightly, while hypoxygen tension stimulates the increase. Data suggest that the cell number destined to be ineffective erythropoiesis is regulated by oxygen tensions of the environment. 2. Basophilic erythroblasts are reduced in number from the beginning showing not any increasing tendency. The reducing rate is almost the same among those cultured under the hypo- and hyperoxygen tension, comparable to that incubated with air. 3. The hypoxygen tension brings about a marked increase in the number of orthochromatic erythroblasts with a decrease in polychromatic erythroblasts suggesting an accelerated cell differentiation, while the hyperoxygen tension elicits the suppression in the formation of orthochromatic erythroblasts with suppressed differentiation. Data also show the lack of denucleation mechanism in polychromatic stages in vitro differing from the case of the bone marrow of anemic animal.</p

Ample canonical heights for endomorphisms on projective varieties

We define an "ample canonical height" for an endomorphism on a projective variety, which is essentially a generalization of the canonical heights for polarized endomorphisms introduced by Call--Silverman. We formulate a dynamical analogue of the Northcott finiteness theorem for ample canonical heights as a conjecture, and prove it for endomorphisms on varieties of small Picard numbers, abelian varieties, and surfaces. As applications, for the endomorphisms which satisfy the conjecture, we show the non-density of the set of preperiodic points over a fixed number field, and obtain a dynamical Mordell--Lang type result on the intersection of two Zariski dense orbits of two endomorphisms on a common variety.Comment: 41 pages. The previous version has a serious mistake on the proof of the main conjecture for simple abelian varieties, but the present version gives a renewed proof that works for arbitrary abelian varietie

Spin Hall Current and Spin-transfer Torque in Ferromagnetic Metal

We theoretically examine the spin-transfer torque in the presence of spin-orbit interaction (SOI) at impurities in a ferromagnetic metal on the basis of linear response theory. We obtained, in addition to the usual spin-transfer torque, a new contributioin $\sim {\bm j}_{\rm SH}^{\phantom{\dagger}} \cdot \nabla {\bm n}$ in the first order in SOI, where ${\bm j}_{\rm SH}^{\phantom{\dagger}}$ is the spin Hall current driven by an external electric field. This is a reaction to inverse spin Hall effect driven by spin motive force in a ferromagnet.Comment: 4 pages, Proceedings of the International Conference on Magnetism, submitted to J. Phys: Conference Serie