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Jun 18, 2024

Classical dynamics of infinite particle systems in an operator algebraic framework

Mathphys Analysis Seminar

Date: June 18, 2024 | 4:15 pm – 5:15 pm
Speaker: Christiaan van de Ven, University of Würzburg
Location: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Language: English

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)

More Information:

Date:
June 18, 2024
4:15 pm – 5:15 pm

Speaker:
Christiaan van de Ven, University of Würzburg

Location:
Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)

Language:
English

Contact:

Oosthuizen-Noczil Birgit

Email:
boosthui@ist.ac.at

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