Finite approximations of physical models over p-adic fields

Bakken, Erik Makino; Digernes, Trond; Lund, M.; Weisbart, David

doi:10.1134/s2070046613040018

Cited by 3 publications

(8 citation statements)

References 6 publications

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“…This article grew out of a desire to explore the utility and effectiveness of stochastic methods in a non-Archimedean setting. In a recent article two of us gave a functional analytic proof of the finite approximability of the Schrödinger operator over a local field [BD15]. In the present article we give a stochastic proof of the same.…”

Section: Introductionmentioning

confidence: 82%

“…Then B n is 1 The rank of a character χ is defined as the largest integer r such that χ| Br ≡ 1. See [BD15] for explicit construction of such characters in the various cases.…”

Section: Basics About Local Fields and Finite Modelsmentioning

confidence: 99%

“…We now collect the basic facts and conventions for the finite level operators (for details, see [BD15]):…”

Section: Basics About Local Fields and Finite Modelsmentioning

confidence: 99%

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Brownian motion and finite approximations of quantum systems over local fields

2017

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We give a stochastic proof of the finite approximability of a class of Schrödinger 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.2010 Mathematics Subject Classification. 81Q65, 60B10, 47G30, 41A99.

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Section: Introductionmentioning

confidence: 82%

“…Then B n is 1 The rank of a character χ is defined as the largest integer r such that χ| Br ≡ 1. See [BD15] for explicit construction of such characters in the various cases.…”

Section: Basics About Local Fields and Finite Modelsmentioning

confidence: 99%

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Brownian motion and finite approximations of quantum systems over local fields

2017

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“…3. Let λ and J be as in (2). Then dim P Mn (J) = dim P M (J) for large n, and for each orthonormal basis {e 1 , .…”

Section: Notationmentioning

confidence: 99%

“…In an earlier article [BDLW13] finite approximations over Q p were treated. The current article supersedes that one; also, the proofs which were omitted there, are given here.…”

Section: Introductionmentioning

confidence: 99%