  The dynamics of correlated systems is relevant in many fields ranging from
cosmology to plasma physics. However, they are challenging to predict and
understand even for classical systems due to the typically large numbers of
particles involved. Here, we study the evolution of an ultracold, correlated
many-body system with repulsive interactions and initial correlations set by
the Rydberg blockade using the analytical framework of Kinetic Field Theory
(KFT). The KFT formalism is based on the path-integral formulation for
classical mechanics and was first developed and successfully used in cosmology
to describe structure formation in Dark Matter. The theoretical framework
offers a high flexibility regarding the initial configuration and interactions
between particles and, in addition, is computationally cheap. More importantly,
the analytic approach allows us to gain better insight into the processes which
dominate the dynamics. In this work we show that KFT can be applied in a much
more general context and study the evolution of a correlated ion plasma. We
find good agreement between the analytical KFT results for the evolution of the
correlation function and results obtained from numerical simulations. We use
the correlation functions obtained with KFT to compute the temperature increase
in the ionic system due to disorder-induced heating. For certain choices of
parameters we observe that the effect can be reversed, leading to correlation
cooling. Due to its numerical efficiency as compared to numerical simulations,
a detailed study using KFT can help to constrain parameter spaces where
disorder-induced heating is minimal in order to reach the regime of strong
coupling.
