Dice Question Streamline Icon: https://streamlinehq.com

Boundary of the stability island around the nonlinear ground state

Determine the equation and precise boundary of the stability island surrounding the self-consistent ground state of the nonlinear Schrödinger equation in the D-shape billiard, and quantify how this boundary constrains the attainable Rayleigh–Jeans condensate fraction and the redistribution of populations among excited modes.

Information Square Streamline Icon: https://streamlinehq.com

Background

The authors identify a self-consistent stationary ground state of the NSE that is dynamically stable, implying the existence of an integrable stability island around it. This stability island limits the fraction of probability that can condense into the linear ground state during thermalization.

Because the exact boundary of this island is unknown, realistic simulations quantifying its effect on condensation are not yet feasible. An explicit description of the boundary would allow precise constraints on the condensate fraction.

References

Since we do not know the equation for the boundary of this stability island we cannot perform realistic simulations, but we checked that simple approximation for the shape of the stability island indeed limit the condensation.

— Dynamical thermalization, Rayleigh-Jeans condensate, vortexes and wave collapse in quantum chaos fibers and fluid of light (2506.06534 - Ermann et al., 6 Jun 2025) in Section 4, Analytical results