Coarse Grained Quantum Dynamics

Understand

Inspired by holographic Wilsonian renormalization, we consider coarse graining a quantum system divided between short distance and long distance degrees of freedom, coupled via the Hamiltonian.

• Observations using purely long distance observables are described by the reduced density matrix that arises from tracing out the short-distance degrees of freedom.
• The dynamics of this density matrix is non-Hamiltonian and nonlocal in time, on the order of some short time scale.
• We describe this dynamics in a model system with a simple hierarchy of energy gaps $\Delta E_{UV} > \Delta E_{IR}$, in which the coupling between high-and low-energy degrees of freedom is treated to second order in perturbation theory.