归一化线性随机薛定谔方程的全局能量解
Global Energy Solutions for Normalized Linear Stochastic Schr{ö}dinger Equations
- CMAP CNRS, Ecole polytechnique, I.P. Paris（巴黎综合理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究马尔可夫开放量子系统中的非线性薛定谔方程，在能量空间中证明线性方程的全局适定性，并在放宽单调性假设下证明非线性SPDE解的不可区分性，最终通过路径唯一性和归一化建立非线性随机方程的适定性。
AI中文摘要：
本文研究了马尔可夫开放量子系统中出现的非线性薛定谔方程。这些方程由线性随机薛定谔方程的归一化推导而来。首先，我们在能量空间中证明了线性方程的全局适定性，该空间比该方程通常使用的空间正则性更低。然后，我们在放宽通常的单调性假设的条件下，证明了非线性SPDE解的不可区分性。最后，通过证明路径唯一性并对线性方程的解进行归一化，我们得以证明所需类别的非线性随机方程的适定性。
英文摘要：
In this paper, we study nonlinear Schr{ö}dinger equations arising in the study of Markovian open quantum systems. These equations are derived from the normalization of linear stochastic Schr{ö}dinger equations. First, we prove the global well-posedness of the linear equation in the energy space, which is less regular than the usual space for this equation. Then, we show the indistinguishability of solutions to the nonlinear SPDE under a relaxation of the usual monotonicity assumption. Finally, by proving the pathwise uniqueness and normalizing the solutions to the linear equation, we are able to prove the well-posedness of solutions to the required class of nonlinear stochastic equations.
