Work

A Microscopic Derivation of Gibbs Measures for the 1D Focusing Quintic Nonlinear Schrödinger Equation

Year: 2025

Type: article

Abstract: . In this work, we obtain a microscopic derivation of Gibbs measures for the focusing quintic nonlinear Schrödinger equation on [Formula: see text] from many-body quantum Gibbs states. On the quantum many-body level, the quintic nonlinearity corresponds to a three-body interaction. This is a continuation of our previous work [A. Rout and V. Sohinger, Comm. Partial Differential Equations, 48 (2023), pp. 1008–1055]. In the aforementioned work, we studied the cubic problem, which corresponds to a two-body interaction on the quantum many-body level. In our setup, we truncate the mass of the classical free field in the classical setting and the rescaled particle number in the quantum setting. Our methods are based on a perturbative expansion previously developed in the work of Fröhlich, Knowles, Schlein, and the second author [ Comm. Math. Phys., 356 (2017), pp. 883–980]. We prove results in both the time-independent and the time-dependent setting.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/24m1681227

Authors: Andrew Rout, Vedran Sohinger

Institutions: Institut de recherche mathématique de Rennes, Université de Rennes, University of Warwick

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Warwick, Engineering and Physical Sciences Research Council

Award: Gibbs measures for nonlinear Schrodinger equations and many-body quantum mechanics