# Collective diffusion and quantum chaos in holography

## TL;DR

This paper explores how a specific 'heat-decoupled' current in holographic models relates charge and heat diffusion to quantum chaos, revealing conditions under which diffusivities are universally connected.

## Contribution

It introduces the concept of a heat-decoupled current and demonstrates its role in linking diffusivities to quantum chaos in holographic theories.

## Key findings

- HD diffusivity can equal charge and heat diffusivities under certain conditions
- Diffusivity/chaos relation holds in some holographic lattices regardless of parameters
- Counterexamples show the limited universality of the diffusivity/chaos relation

## Abstract

We define a particular combination of charge and heat currents that is decoupled with the heat current. This `heat-decoupled' (HD) current can be transported by diffusion at long distances, when some thermo-electric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z=2. In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.