Cauchy semigroups: Nonlocally induced bound states
主 题: Cauchy semigroups: Nonlocally induced bound states
报告人: Prof.Piotr Garbaczewski (University of Opole )
时 间: 2015-06-01 15:00 - 16:00
地 点: 英国威廉希尔公司理科一号楼 1493
Generators of Lévy jump-type processes are spatially nonlocal. This becomes an issue if a nonlocally induced random motion is to be confined in a finite trapping enclosure. We address a prototype example of the Cauchy process in the interval (-1,1), with a focus on spectral properties of the motion generator. We provide a detailed analysis of how an approximate functional shape of lowest eigenfunctions can be recovered and how this outcome fidelity is related to the evaluation finesse of the corresponding eigenvalues. As a byproduct of the discussion we identify a probability preserving stochastic process in a trap whose asymptotic (stationary) probability distribution, upon normalization, is determined by the squared ground state functio
