Invariant measure for the Schrödinger equation on the real line

DOI10.1016/j.jfa.2015.04.021zbMath1317.35227arXiv1405.5107OpenAlexW657430203MaRDI QIDQ2344857

Anne-Sophie de Suzzoni, Federico Cacciafesta

Publication date: 18 May 2015

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.5107

zbMATH Keywords

invariant measuresSchrödinger equation

Mathematics Subject Classification ID

Brownian motion (60J65) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (11)

Gibbs measure for the higher order modified Camassa-Holm equation ⋮ Stability of invariant measures and continuity of the KdV flow ⋮ Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions \({d \leqslant 3}\) ⋮ Invariance of Gibbs measures under the flows of Hamiltonian equations on the real line ⋮ Randomization and the Gross-Pitaevskii hierarchy ⋮ Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits ⋮ Invariant measures for complex-valued dissipative dynamical systems and applications ⋮ Classical field theory limit of many-body quantum Gibbs states in 2D and 3D ⋮ Global well posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain ⋮ Gibbs Measures of Nonlinear Schrödinger Equations as Limits of Quantum Many-Body States in Dimension d ≤ 3 ⋮ Invariant measures for the two-dimensional averaged-Euler equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below \(L^{2}(\mathbb{T})\)
• Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
• Almost sure well-posedness for the periodic 3D quintic nonlinear Schrödinger equation below the energy space
• Invariant Gibbs measures and a.s. global well posedness for coupled KdV systems.
• Random data Cauchy theory for supercritical wave equations. II. A global existence result
• Random data Cauchy theory for supercritical wave equations I: Local theory
• Invariant measures for the defocusing nonlinear Schrödinger equation
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Statistical mechanics of the nonlinear Schrödinger equation
• Periodic nonlinear Schrödinger equation and invariant measures
• Two-dimensional nonlinear Schrödinger equation with random radial data
• Invariant measures for NLS in infinite volume
• Absolute continuity of Brownian bridges under certain gauge transformations
• Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on ℝ³
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS

This page was built for publication: Invariant measure for the Schrödinger equation on the real line