Islands of Instability in Nonlinear Wavefunction Models in the Continuum: A Different Route to "Chaos"
W. David Wick
TL;DR
The paper investigates islands of instability in nonlinear wavefunction dynamics within a three-dimensional continuum framework that includes inter-molecular potentials. By deriving computable bounds on the positive eigenvalue $\lambda_{\max}$ via test functions, it extends instability criteria from finite systems to continuum models, using Lennard-Jones-type and Basuev integrable potentials. It shows that simple nearly-classical states fail to generate instability at large $N$, but spatial superpositions in the large-N regime can produce parameter ranges where instability criteria may be satisfied, and it develops a discrete-to-continuum bounding strategy through resolvent convergence to justify persistence of instability in the continuum limit. The findings illuminate potential links to measurement crises and, more broadly, to macroscopic phenomena such as turbulence, while outlining methodological paths for applying the approach to realistic fluids and gases. Overall, the work provides a practical framework to assess nonlinear instability in continuum wavefunction models beyond exactly solvable cases, with implications for understanding chaos-like behavior in complex media.
Abstract
In two previous papers the author described ``Islands of Instability" that may appear in wavefunction models with nonlinear evolution (of a type proposed originally in the context of the Measurement Problem). Such ``IsoI" represent a new scenario for Hamiltonian systems implying so-called ``chaos". Criteria was derived for, and shown to be fulfilled in, some finite-dimensional (multi-qubit) models, and generalized in the second paper to continuum models. But the only example produced of the latter was a model whose linear Schrodinger equation was exactly-solvable. As exact solutions of many-body problems are rare, here I show that the instability criteria can be verified by plugging test-functions into certain computable expressions, bypassing the solvability blockade. The method can accommodate realistic inter-molecular potentials and so may be relevant to instabilities in fluids and gasses.