Year: 2026
Type: article
Abstract: We consider the Gibbs measure for the focusing nonlinear Schrödinger equation on the one-dimensional torus $${\mathbb {T}}$$ T , that was introduced in a seminal paper by Lebowitz et al. (J Stat Phys 50(3):657—687, 1988). We show that in the large torus limit, the measure exhibits a phase transition, depending on the size of the nonlinearity. This phase transition was originally conjectured on the basis of numerical simulation by Lebowitz et al. (J Stat Phys 50(3):657—687, 1988). Its existence is however striking in view of a series of negative results by McKean (Commun Math Phys 168(3):479—491, 1995) and Rider (Commun Pure Appl Math 55(10):1231—1248, 2002).
Authors: Leonardo Tolomeo, Hendrik Weber
Institutions: University of Edinburgh, University of Münster
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W7140185509