1D Chain Cascade
This page describes my attempt to understand the dynamics of Bose relaxation down a cascade of modes, following the impromptu discovery of a sudden collapse of the population in the ground state when trying to convince my Chinese colleagues that their Monte Carlo code was inefficient, and asking Claude to prove that by demonstrating a case.
One question is whether the quantum-Boltzmann aspect is important for this phenomenology. If not, the phenomenon is certainly known in other context. If so, it's definitely interesting as providing more physics to Alexey's Bosonic cascades,[1] since this is exactly the physics at play.
The effect weakens as the chain lengthens. Defining Φφ6666φ At M=160 collapses to 0.11: the ground mode fills gradually over two decades with no burst. The natural reading is a competition between stimulated growth (~$w n_1$) and the spread in arrival times of particles crossing M modes — short chains deliver simultaneously and run away, long chains trickle and growth merely keeps pace. If so, Φ should collapse onto one combination of M and T, and finding it would be a real result rather than an observation.