Rainbow Nambu-Goldstone modes under a shear flow

TL;DR

This paper investigates how shear flow affects Nambu-Goldstone modes in an $O(N)$ scalar model, revealing a novel rainbow pattern with fractional dispersion relations not seen in equilibrium.

Contribution

It introduces the concept of rainbow Nambu-Goldstone modes, showing their splitting into infinitely many gapless modes with unique dispersion under shear flow.

Findings

Nambu-Goldstone modes split into infinitely many gapless modes.

Modes exhibit fractional dispersion relation $\, ext{omega} \,\,\sim \,k_1^{2/3}$.

Behavior is distinct from equilibrium states.

Abstract

We study an $O(N)$ scalar model under shear flow and its Nambu-Goldstone modes associated with spontaneous symmetry breaking $O(N) \to O(N-1)$. We find that the Nambu-Goldstone mode splits into an infinite number of gapless modes, which we call the rainbow Nambu-Goldstone modes. They have different group velocities and the fractional dispersion relation $\omega \sim k_1^{2/3}$, where $k_1$ is the wavenumber along the flow. Such behaviors do not have counterparts in an equilibrium state.