Anomalous Hydrodynamics in One Dimensional Electronic Fluid

TL;DR

This paper develops a multi-mode viscous hydrodynamics framework for one-dimensional electronic fluids, revealing anomalous scaling behaviors and wave broadening phenomena across different length scales.

Contribution

It introduces a novel multi-mode hydrodynamic model capturing anomalous scaling and wave propagation in 1D electronic fluids, including KPZ-like broadening and Levy flight effects.

Findings

All modes exhibit KPZ-like broadening at certain scales.

Thermal conductivity scales as ^{-1/3} due to Levy flight behavior.

Different regimes show distinct hydrodynamic mode structures.

Abstract

We construct multi-mode viscous hydrodynamics for one dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In a four-mode regime, all modes are ballistic and acquire KPZ-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to $\omega^{-1/3}$ scaling of its real part. In a three-mode regime, the system is in the universality class of classical viscous fluid[9,24]. Self-interaction of the sound modes results in KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to $\omega^{-1/3}$ scaling of heat conductivity.