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Register a new userBrownian Motion and Finite Approximations of Quantum Systems over Local Fields
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We give a stochastic proof of the finite approximability of a class of Schru007fodinger 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.
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We show that the Schrodinger operator associated with a physical system over a local field can be approximated in a very strong sense by finite Schrodinger operators. Some striking numerical results are included at the end of the article.
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