Abstract
We study the open system dynamics of a harmonic oscillator "system" coupled to an "environment" of oscillators with an exponential density of states, motivated by holographic models of non-gravitational "little" string theories. We present the Heisenberg equations of motion and the quantum master equation for the system, and develop a renormalization procedure to manage the divergences, which are exponential in the cutoff. We provide evidence that the renormalized system dynamics is Markovian even when the initial state of the environment is the instantaneous ground state.