Brownian Motion and Finite Approximations of Quantum Systems over Local Fields
Mathematical Physics
2017-06-28 v1 math.MP
Abstract
We give a stochastic proof of the finite approximability of a class of Schr\"odinger operators over a local field, thereby completing a program of establishing in a non-Archimedean setting corresponding results and methods from the Archimedean (real) setting. A key ingredient of our proof is to show that Brownian motion over a local field can be obtained as a limit of random walks over finite grids. Also, we prove a Feynman-Kac formula for the finite systems, and show that the propagator at the finite level converges to the propagator at the infinite level.
Keywords
Cite
@article{arxiv.1612.03114,
title = {Brownian Motion and Finite Approximations of Quantum Systems over Local Fields},
author = {Erik M. Bakken and Trond Digernes and David Weisbart},
journal= {arXiv preprint arXiv:1612.03114},
year = {2017}
}