# The resolvent algebra for oscillating lattice systems: Dynamics, ground and equilibrium states

May 17, 2016

Within the framework of the resolvent algebra, the structure of oscillating
lattice systems with bounded nearest neighbor interactions in any number of
dimensions is studied. It is shown that the global dynamics of such systems
acts on the resolvent algebra by automorphisms and that equilibrium (KMS)
states as well as ground states exist which are regular (locally normal). It is
also indicated how to deal with unbounded interactions and non-harmonic
oscillations.

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