Nonlinear Regime of the Quantum Three Wave Interaction*

The three-wave interaction, the lowest order nonlinear interaction in plasma physics, describes energy-momentum transfer between three resonant waves in the quantum regime; however, it may also act as a finite-degree-of-freedom approximation of the classical three-wave interaction in certain circumstances. Using the quantum field theoretic quantization scheme, recently used to model the interaction on a quantum computer [1], we build on work describing the quantum three-wave instability near the classical fixed point to show how quantum scrambling near hyperbolic points in the quantum system inhibit long-term correspondence with the classical system [2]. We also numerically compare the long-time quantum/classical correspondence far from the fixed point dynamics, where the systems have been shown to become harmonic.

[1] Y. Shi, H. Qin, and N. Fisch, Phys. Plamsas 28, 042104 (2021).
[2] M. Q. May and H. Qin, Phys. Rev. A 107, 062204 (2023).