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We define a particular combination of charge and heat currents that isdecoupled with the heat current. This `heat-decoupled' (HD) current can betransported by diffusion at long distances, when some thermo-electricconductivities and susceptibilities satisfy a simple condition. Using thediffusion condition together with the Kelvin formula, we show that the HDdiffusivity can be same as the charge diffusivity and also the heatdiffusivity. We illustrate that such mechanism is implemented in a stronglycoupled field theory, which is dual to a Lifshitz gravity with the dynamicalcritical index z=2. In particular, it is exhibited that both charge and heatdiffusivities build the relationship to the quantum chaos. Moreover, we studythe HD diffusivity without imposing the diffusion condition. In somehomogeneous holographic lattices, it is found that the diffusivity/chaosrelation holds independently of any parameters, including the strength ofmomentum relaxation, chemical potential, or temperature. We also show a counterexample of the relation and discuss its limited universality.

Collective diffusion and quantum chaos in holography