Mean first passage time for fission potentials having structure

A schematic model of over-damped motion is presented which permits one to calculate the mean first passage time for nuclear fission. Its asymptotic value may exceed considerably the lifetime suggested by Kramers rate formula, which applies only to very special, favorable potentials and temperatures. The additional time obtained in the more general case is seen to allow for a considerable increment in the emission of light particles.Comment: 7 pages, LaTex, 7 postscript figures; Keywords: Decay rate, mean first passage tim

Statistics of the first passage time of Brownian motion conditioned by maximum value or area

We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework. Various applications are indicated.Comment: 29 pages, 4 figures include

Random Walk with Shrinking Steps: First Passage Characteristics

We study the mean first passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like $\lambda^{n}$ with $\lambda\leq1$ . We also present, for pedagogical purposes, a continuum system with a diffusion constant decaying exponentially in continuous time. Qualitatively both systems are alike in their global properties. However, the discrete case shows very rich mathematical structure, depending on the value of the shrinking parameter, such as self-repetitive and fractal-like structure for the first passage characteristics. The results we present show that the most important quantitative behavior of the discrete case is that the support of the distribution function evolves in time in a rather complicated way in contrast to the time independent lattice structure of the ordinary random walker. We also show that there are critical values of $\lambda$ defined by the equation $\lambda^{K}+2\lambda^{P}-2=0$ with $\{K,N\}\in{\mathcal N}$ where the mean first passage time undergo transitions.Comment: Major Re-Editing of the article. Conclusions unaltere