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Classical dynamics of infinite particle systems in an operator algebraic framework

Mathphys Analysis Seminar

Date: Tuesday, June 18, 2024 16:30 - 17:30
Speaker: Christiaan van de Ven (University of W├╝rzburg)
Location: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Robert Seiringer

In this seminar I present a study on the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, as well on more general structures; and I show that this enables the construction of C*-dynamical systems. This approach allows particles with varying masses, varying frequencies, irregularly placed lattice sites and varying interactions subject to a simple summability constraint. A key role is played by the commutative resolvent algebra, which is a C*-algebra of bounded continuous functions on an infinite dimensional vector space, and in a strong sense the classical limit of the Buchholz-Grundling resolvent algebra, which suggests that quantum analogs of our results are likely to exist. For a general class of Hamiltonian dynamics, it is demonstrated that this algebra is time-stable, and admits a time-stable sub-algebra on which the dynamics is strongly continuous, therefore obtaining a C*-dynamical system. Joint work with van Nuland (TU Delft)

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