2023/09/12 by Teun D. H. van Nuland, van Nuland, T. D. H., Christiaan J. F. van de Ven +1 · 1 citation
Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2309.06242
openalex publication_date 2023/09/12 · openalex created_date 2023/09/14 · openalex updated_date 2026/07/28
We construct C*-dynamical systems for the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, as well on more general structures. Our 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 Hamiltonians, we show that the commutative resolvent algebra is time-stable, and admits a time-stable sub-algebra on which the dynamics is strongly continuous, therefore obtaining a C*-dynamical system.