Geodesic
Models of $p$-adic mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 285-291 Cet article a éte moissonné depuis la source Math-Net.Ru

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We segregate the class of ultrametric ($p$-adic) systems within the standard models of classical and quantum mechanics. We show that ultrametric models can be described in the language of standard models but also have several distinguishing properties. In particular, we show that a stronger Poincaré recurrence theorem holds for classical ultrametric dynamical systems. As an example of a quantum $p$-adic system, we consider the algebra of commutation relations of the one-dimensional quantum mechanics. We show that this algebra, as in the real case, is isomorphic to the algebra of compact operators.
Keywords: ultrametric, $p$-adic classical mechanics, $p$-adic quantum mechanics. 
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E. I. Zelenov. Models of $p$-adic mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 285-291. http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a7/

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