Discrete bound states in a toy model for weak turbulence and implications for the invariant measure
Abstract
A model Hamiltonian dynamical system has been derived to study frequency cascades in the cubic defocusing nonlinear Schrödinger equation on the torus. Here, we explore the framework for exploring a canonical ensemble formulation of the dynamics through classification of energy minimizers for fixed mass and characterizing the invariant measure in a neighborhood of those minimizers.
Fields of Study & Subjects
Nonlinear Photonic Systems
Quantum chaos and dynamical systems
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Communications in Mathematical Sciences
- Publisher
- International Press of Boston
- Volume
- 24
- Issue
- 6
- Pages
- 1635–1667
- Publication date
- 1 January 2026
- Language
- EN