Steady States, Thermal Physics, and Holography

Figure 7

A schematic representation of the chaos diagnostic function(s). Here, qualitatively, , while both and individually carry the information of an exponential decay (for ) or growth (for ) of the corresponding correlator. The exponential behaviour occurs in a regime between a time-scale, such as the dissipation time , and a parametrically large time-scale, such as the scrambling time . This hierarchy of and is ensured in the limit.