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

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

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

The boundary of the moduli space of stable cubic fivefolds

By GIT theory due to Mumford, the moduli space of stable cubic fivefolds is compactified by adding non stable semi-stable (i.e. strictly semi-stable) locus. In this paper, we prove that this locus consists of 19 components. Moreover, we give a description of equation and singularity of cubic fivefold corresponding to the generic point in each component.Comment: 14 page

Emulsion chamber observations and interpretation (HE 3)

Experimental results from Emulsion Chamber (EC) experiments at mountain altitudes or at higher levels using flying carriers are examined. The physical interest in this field is concentrated on the strong interaction at the very high energy region exceeding the accelerator energy, also on the primary cosmic ray intensity and its chemical composition. Those experiments which observed cosmic ray secondaries gave information on high energy interaction characteristics through the analyses of secondary spectra, gamma-hadron families and C-jets (direct observation of the particle production occuring at the carbon target). Problems of scaling violation in fragmentation region, interaction cross section, transverse momentum of produced secondaries, and some peculiar features of exotic events are discussed