Continuous-wave solutions and modulational instability in spinor condensates of positronium

TL;DR

This paper analyzes continuous-wave solutions and modulational instability in spinor positronium condensates, revealing stability conditions based on particle density, spin component interactions, and wavenumber differences.

Contribution

It provides a comprehensive analysis of CW solutions and MI in spinor positronium condensates, including stability criteria and effects of population exchange and wavenumber differences.

Findings

CW solutions exist with both in-phase and out-of-phase spin components.

Stability depends on particle density and spin component interactions.

MI occurs when wavenumber differences are non-zero, affecting condensate stability.

Abstract

We obtain general continuous-wave (CW)\ solutions in the model of a spinor positronium condensate in the absence of magnetic field. The CW solutions with both in-phase ($n=0$) and out-of-phase ($n=1$) spin components exist, with their ranges limited by the total particle density, $\rho $. In the limit of negligible population exchange between the spin components, the CW solutions are found to be stable or unstable, depending on the particle density of the para positronium. Ortho positronium, in the $F=1$ spinor state, forms a ferromagnetic condensate with stable in-phase CW solutions only. Subsequent examination of the modulational instability (MI) is carried out both in the limit case of identical wavenumbers in the spin components, $% \Delta k\equiv k_{1}-k_{-1}=0$, and in the more general case of $\Delta k\neq 0$ too. The CW solutions with $n=0$ and $1$ solutions, which are stable in the case of $\Delta k=0$, are unstable for $\Delta k\neq 0$, for the natural repulsive sign of the nonlinearities. The total particle density, $\rho $, in the limit of $\Delta k=0$ is found to have a significant role for the stability of the condensate, which is determined by the sign of the self-interaction nonlinearity.