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 Abstract:   We study the unitary dynamics of operators in a chaotic many-body system with a locally conserved quantity like charge or energy that moves diffusively.   The results shed some light on the mechanism by which unitary quantum dynamics, which is reversible, gives rise to diffusive transport, which is a dissipative process.  We obtain our results in a random quantum circuit model that has a conservation law.  We find that a generic local operator consists of two parts: (i) a conserved part which comprises the weight of the operator on the local conserved densities, whose dynamics is described by diffusion.   This conserved part also acts as a source that steadily emits a flux of (ii) non-conserved operators that then rapidly spread and become highly nonlocal and thus effectively not “observable”.  This emission is at a rate set by the local diffusion current.   We can also follow the unitary dynamics of the non-conserved component of the operator and see it spreading at a Lieb-Robinson speed, but with diffusive corrections due to the conserved part of the operator that is “left behind” and whose weight decays as a power of time.

Ref.:  Khemani, Vishwanath and Huse, arXiv:1710.09835.