Islands of Instability in Nonlinear Wavefunction Models in the Continuum: A Different Route to "Chaos"

TL;DR

This paper introduces a practical method to verify instability criteria in nonlinear wavefunction models, enabling analysis of complex continuum systems beyond exactly solvable cases, with potential applications in fluid and gas dynamics.

Contribution

It presents a new approach to verify islands of instability in nonlinear continuum wavefunction models without requiring exact solutions.

Findings

Instability criteria can be tested using test-functions and computable expressions.

Method accommodates realistic inter-molecular potentials.

Applicable to complex systems like fluids and gases.

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.