Flavor solitons in dense neutrino gases

TL;DR

The paper investigates nonlinear flavor evolution in dense neutrino gases within the fast-flavor limit and identifies exact soliton solutions of the nonlinear flavor-wave equation. By leveraging a pendulum analogy, Lax-vector formalism, and Lorentz boosts, it uncovers temporal solitons (one-swing pendulums), spatial solitons (static in space), and uniformly moving (super- or subluminal) solitons, all tied to a crossed-spectrum condition and a Nyquist-based stability criterion. It also analyzes matter effects, showing that only temporal solitons can survive in a frame comoving with matter, while static and subluminal solitons are generally destabilized. Overall, the work reveals a rich, highly structured nonlinear dynamics in fast flavor oscillations and clarifies the limitations of soliton solutions in realistic environments.

Abstract

We consider a dense neutrino gas in the "fast-flavor limit" (vanishing neutrino masses). For the first time, we identify exact solutions of the nonlinear wave equation in the form of solitons. They can propagate with both sub- or superluminal speed, the latter not violating causality. The soliton with infinite speed is a homogeneous solution and coincides with the usual fast-flavor pendulum except that it swings only once instead of being periodic. The subluminal soliton in the static limit corresponds to a one-swing "spatial pendulum". A necessary condition for such solutions to exist is a ``crossed'' neutrino angle distribution. Based on the Nyquist criterion, we derive a new sufficient condition without solving the dispersion relation. The solitons are very fragile: they are as unstable as the homogeneous neutrino gas alone. Moreover, in the presence of matter, only the solution survives that is homogeneous in a frame comoving with the matter current. Generally, the matter effect cannot be eliminated by transformations in flavor space, but instead has a real physical impact.

Figures (7)

• Figure 1: Components of ${\bf D}_1(t)$ for our two benchmark cases of three-beam systems defined in Table \ref{['tab:examples']}.
• Figure 3: Components of ${\bf D}_1(t)$ for a temporal soliton for our benchmark cases with parameters given in Table \ref{['tab:examples']}. The $D_1^z$ component stays flat for $t\to\pm\infty$, whereas the transverse components continue to shrink exponentially for $t\to\pm\infty$ towards the unstable fixed point.
• Figure 5: Structure of the superluminal soliton as a function of the comoving coordinate $r-v_\mathrm{soliton} t$ for a superluminal soliton velocity $v_\mathrm{soliton}=V^{-1}=2.857$, for the two reference cases defined in Table \ref{['tab:examples']}. Here $V=0.35$ is the speed of the frame in which the soliton is homogeneous. In the original frame, ${\bf D}_0$ and $|{\bf D}_1|$ are no longer conserved.
• Figure 6: Imaginary part of the comoving-frame frequency $\Omega'$ as a function of the soliton speed $v_\mathrm{soliton}=V^{-1}$ for the two benchmark cases defined in Table \ref{['tab:examples']}.
• Figure 7: Evolution of an initial soliton with velocity $V=0.1$. The color intensity denotes time.