Phase transition for invariant measures of the focusing Schrödinger equation
Tolomeo, Leonardo; Weber, Hendrik
Research article in digital collection | Preprint | Peer reviewedAbstract
In this paper, we consider the Gibbs measure for the focusing nonlinear Schrödinger equation on the one-dimensional torus, that was introduced in a seminal paper by Lebowitz, Rose and Speer (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, Rose and Speer (1988). Its existence is however striking in view of a series of negative results by McKean (1995) and Rider (2002).
Details about the publication
Name of the repository: arXiv
Article number: 2306.07697
Status: Published
Release year: 2023
Link to the full text: https://arxiv.org/abs/2306.07697
Keywords: nonlinear Schrödinger equation; phase transition; numerical simulation; Gibbs measure
Authors from the University of Münster
| Weber, Hendrik | Professorship of Mathematics (Prof. Weber) |