Hydrodynamic approach to transport and quantum turbulence in nanoscale conductors

TL;DR

This paper proposes a hydrodynamic model for electron transport in nanoscale conductors, simplifying the complex electron-electron interactions by describing the flow with Navier-Stokes equations and predicting conditions for turbulence.

Contribution

It introduces a novel hydrodynamic framework for electron transport in nanoscale systems, linking quantum electron flow to classical fluid dynamics.

Findings

Electron flow can be modeled by Navier-Stokes equations with an effective viscosity.

Conditions for laminar-turbulent transition in nanoscale conductors are derived.

Experimental tests for the hydrodynamic behavior are discussed.

Abstract

The description of electron-electron interactions in transport problems is both analytically and numerically difficult. Here we show that a much simpler description of electron transport in the presence of interactions can be achieved in nanoscale systems. In particular, we show that the electron flow in nanoscale conductors can be described by Navier-Stokes type of equations with an effective electron viscosity, i.e., on a par with the dynamics of a viscous and compressible classical fluid. By using this hydrodynamic approach we derive the conditions for the transition from laminar to turbulent flow in nanoscale systems and discuss possible experimental tests of our predictions.