AG Mathematische Physik, Nicolò Drago (Genua): Classical and quantum KMS states on spin lattice systems

Nicolò Drago (Genua)

Classical and quantum KMS states on spin lattice systems

Abstract: We study the classical and quantum KMS conditions within
the context of spin lattice systems. Specifically, we define a strict
deformation quantization (SDQ) for a S^2-valued spin lattice system over
Z^d generalizing the renown Berezin SDQ for
a single sphere. This allows to promote a classical dynamics on the
algebra of classical observables to a quantum dynamics on the algebra of
quantum observables. We then compare the notion of classical and
quantum thermal equilibrium by showing that any weak*-limit
point of a sequence of quantum KMS states fulfils the classical KMS
condition. In short, this proves that the semiclassical limit of quantum
thermal states describes classical thermal equilibrium, strengthening
the physical interpretation of the classical
KMS condition. Finally we provide two sufficient conditions ensuring
uniqueness of classical and quantum KMS states: The latter are based on a
version of the Kirkwood-Salzburg equations adapted to the system of
interest. As a consequence we identify a mild
condition which ensures uniqueness of classical KMS states and of
quantum KMS states for the quantized dynamics for a common sufficiently
high temperature.

Joint work with L. Pettinari and C.J.F. van de Ven.