Momentum dissipation and effective theories of coherent and incoherent transport

TL;DR

This paper investigates heat transport in systems without momentum conservation, revealing how the rate of momentum dissipation influences coherent and incoherent transport regimes, with exact holographic calculations at critical dissipation.

Contribution

It provides a detailed analysis of heat transport regimes based on momentum dissipation rates and derives exact Green's functions for a holographic system at a critical dissipation point.

Findings

Coherent transport exhibits a sound-like mode at slow momentum dissipation.

Incoherent transport is purely diffusive at fast momentum dissipation.

Exact Green's functions are obtained at a critical dissipation rate due to emergent symmetries.

Abstract

We study heat transport in two systems without momentum conservation: a hydrodynamic system, and a holographic system with spatially dependent, massless scalar fields. When momentum dissipates slowly, there is a well-defined, coherent collective excitation in the AC heat conductivity, and a crossover between sound-like and diffusive transport at small and large distance scales. When momentum dissipates quickly, there is no such excitation in the incoherent AC heat conductivity, and diffusion dominates at all distance scales. For a critical value of the momentum dissipation rate, we compute exact expressions for the Green's functions of our holographic system due to an emergent gravitational self-duality, similar to electric/magnetic duality, and SL(2,R) symmetries. We extend the coherent/incoherent classification to examples of charge transport in other holographic systems: probe brane theories and neutral theories with non-Maxwell actions.