测量非线性噪声驱动的随机Schrödinger晶格系统的吸引子

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-05-30 DOI:10.1016/j.bulsci.2025.103672

Shaoyue Mi , Ran Li , Dingshi Li

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引用次数: 0

摘要

研究了ZN上无限维非线性噪声驱动的随机Schrödinger方程的测度吸引子。我们首先介绍了测度吸引子的基本概念和这类系统的渐近紧性。随后，我们建立了测度吸引子的存在唯一性和结构性质的一般定理。最后，我们应用这个抽象框架来分析随机Schrödinger格系统的测度吸引子。

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Measure attractors of stochastic Schrödinger lattice systems driven by nonlinear noise

This paper focuses on the measure attractors of stochastic Schrödinger equations driven by infinite-dimensional nonlinear noise on

Z^{N}

. We begin by introducing the fundamental concepts of measure attractors and the asymptotic compactness of such systems. Subsequently, we establish a general theorem concerning the existence, uniqueness, and structural properties of measure attractors. Finally, we apply this abstract framework to analyze the measure attractors of stochastic Schrödinger lattice systems.

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