Hasimoto frames and the Gibbs measure of periodic nonlinear Schrödinger equation

Blower, Gordon and Khaleghi, Azadeh and Kuchemann-Scales, Moe (2022) Hasimoto frames and the Gibbs measure of periodic nonlinear Schrödinger equation. Working Paper. Arxiv.

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Abstract

The paper interprets the cubic nonlinear Schr\"odinger equation as a Hamiltonian system with infinite dimensional phase space. There is a Gibbs measure which is invariant under the flow associated with the canonical equations of motion. The logarithmic Sobolev and concentration of measure inequalities hold for the Gibbs measures, and here are extended to the $k$-point correlation function and distributions of related empirical measures. By Hasimoto's theorem, NLSE gives a Lax pair of coupled ODE for which the solutions give a system of moving frames. The paper studies the evolution of the measure induced on the moving frames by the Gibbs measure.

Item Type:
Monograph (Working Paper)
Additional Information:
ArXiv: 2205.12868
Uncontrolled Keywords:
Data Sharing Template/no
Subjects:
?? concentration of measureempirical processesstatistical mechanicsno ??
ID Code:
182947
Deposited By:
Deposited On:
17 Jan 2023 16:35
Refereed?:
No
Published?:
Published
Last Modified:
16 Jul 2024 08:01