20 research outputs found
A time-dependent perturbative analysis for a quantum particle in a cloud chamber
We consider a simple model of a cloud chamber consisting of a test particle
(the alpha-particle) interacting with two other particles (the atoms of the
vapour) subject to attractive potentials centered in . At time zero the alpha-particle is described by an outgoing
spherical wave centered in the origin and the atoms are in their ground state.
We show that, under suitable assumptions on the physical parameters of the
system and up to second order in perturbation theory, the probability that both
atoms are ionized is negligible unless lies on the line joining the
origin with . The work is a fully time-dependent version of the original
analysis proposed by Mott in 1929.Comment: 23 page
Quasiclassical mass spectrum of the black hole model with selfgravitating dust shell
We consider a quantum mechanical black hole model introduced in {\it
Phys.Rev.}, {\bf D57}, 1118 (1998) that consists of the selfgravitating dust
shell. The Schroedinger equation for this model is a finite difference equation
with the shift of the argument along the imaginary axis. Solving this equation
in quasiclassical limit in complex domain leads to quantization conditions that
define discrete quasiclassical mass spectrum. One of the quantization
conditions is Bohr-Sommerfeld condition for the bound motion of the shell. The
other comes from the requirement that the wave function is unambiguously
defined on the Riemannian surface on which the coefficients of Schroedinger
equation are regular. The second quantization condition remains valid for the
unbound motion of the shell as well, and in the case of a collapsing null-dust
shell leads to spectrum.Comment: 35 pages, 8 figures, to appear in Phys. Rev.
From Vicious Walkers to TASEP
We propose a model of semi-vicious walkers, which interpolates between the
totally asymmetric simple exclusion process and the vicious walkers model,
having the two as limiting cases. For this model we calculate the asymptotics
of the survival probability for particles and obtain a scaling function,
which describes the transition from one limiting case to another. Then, we use
a fluctuation-dissipation relation allowing us to reinterpret the result as the
particle current generating function in the totally asymmetric simple exclusion
process. Thus we obtain the particle current distribution asymptotically in the
large time limit as the number of particles is fixed. The results apply to the
large deviation scale as well as to the diffusive scale. In the latter we
obtain a new universal distribution, which has a skew non-Gaussian form. For
particles its asymptotic behavior is shown to be
as and
as .Comment: 37 pages, 4 figures, Corrected reference