Research Paper#Stochastic Differential Equations, Nonlinear Schrödinger Equation, Mixing Properties🔬 ResearchAnalyzed: Jan 3, 2026 08:53
Polynomial Mixing for Stochastic Schrödinger Equation
Published:Dec 31, 2025 03:42
•1 min read
•ArXiv
Analysis
This paper investigates the long-time behavior of the stochastic nonlinear Schrödinger equation, a fundamental equation in physics. The key contribution is establishing polynomial convergence rates towards equilibrium under large damping, a significant advancement in understanding the system's mixing properties. This is important because it provides a quantitative understanding of how quickly the system settles into a stable state, which is crucial for simulations and theoretical analysis.
Key Takeaways
- •Focuses on the stochastic nonlinear Schrödinger equation in the whole space.
- •Establishes polynomial convergence rates to equilibrium under large damping.
- •Uses a coupling strategy with pathwise Strichartz estimates.
- •Addresses the mixing property of the equation.
Reference
“Solutions are attracted toward the unique invariant probability measure at polynomial rates of arbitrary order.”