Theory of non-linear diffusion with a physical gapped mode

Abstract

In a system with one conserved charge the charge diffusion is modified by non-linear self-interactions within an effective field theory (EFT) of diffusive fluctuations. We include the slowest ultraviolet (UV) mode, constructing a UV-regulated EFT. The relaxation time of this UV mode is protected from renormalization, as supported by experimental data in a bad metal system. Furthermore, the retarded density-density Green's function acquires four branch points, eventually increasing the range of applicability. We discuss the fate of long-time-tails as well as implications for the quark gluon plasma.

Comments: 8 pages + 4 appendices, 7 figures, comments welcome; v2: Figure 2 improved, Figure 3 and discussion on fitting reference [11] data to our model added, references added