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

Non-Abelian Dual Superconductor Picture for Quark Confinement

We give a theoretical framework for defining and extracting non-Abelian magnetic monopoles in a gauge-invariant way in SU(N) Yang-Mills theory to study quark confinement. Then we give numerical evidences that the non-Abelian magnetic monopole defined in this way gives a dominant contribution to confinement of fundamental quarks in SU(3) Yang-Mills theory, which is in sharp contrast to the SU(2) case in which Abelian magnetic monopoles play the dominant role for quark confinement.Comment: 9 pages, 3 figures (4 ps files); The paper was extensively revised, focusing especially on the lattice par

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

Stability of rigidly rotating relativistic stars with soft equations of state against gravitational collapse

We study secular stability against a quasi-radial oscillation for rigidly rotating stars with soft equations of state in general relativity. The polytropic equations of state with polytropic index $n$ between 3 and 3.05 are adopted for modeling the rotating stars. The stability is determined in terms of the turning-point method. It is found that (i) for n \agt 3.04, all the rigidly rotating stars are unstable against the quasi-radial oscillation and (ii) for n \agt 3.01, the nondimensional angular momentum parameter $q \equiv cJ/GM^2$ (where $J$, $M$, $G$, and $c$ denote the angular momentum, the gravitational mass, the gravitational constant, and the speed of light, respectively) for all marginally stable rotating stars is larger than unity. A semi-analytic calculation is also performed, and good agreement with the numerical results is confirmed. The final outcome after axisymmetric gravitational collapse of rigidly rotating and marginally stable massive stars with $q > 1$ is predicted, assuming that the rest-mass distribution as a function of the specific angular momentum is preserved and that the pressure never halt the collapse. It is found that even for 1 < q \alt 2.5, a black hole may be formed as a result of the collapse, but for q \agt 2.5, the significant angular momentum will prevent the direct formation of a black hole.Comment: 23 pages, to be published in Ap