Measure attractors of stochastic Schrödinger lattice systems driven by nonlinear noise

Abstract

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.