标题： 经典噪声对量子二能级系统的影响 显示英文标题

标题： The effect of classical noise on a quantum two-level system

摘要： 我们考虑一个由经典噪声扰动的量子二能级系统。 噪声被实现为哈密顿矩阵非对角元素中的平稳扩散过程，代表横向磁场。 我们确定系统的不变测度并证明其唯一性。 在奥恩斯坦-乌伦贝克噪声的情况下，我们确定收敛到不变测度的速度。 最后，我们确定一个近似的二维扩散方程用于转移概率。 证明同时使用了谱理论和概率方法。 显示英文摘要

摘要： We consider a quantum two-level system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the off-diagonal matrix elements of the Hamiltonian, representing a transverse magnetic field. We determine the invariant measure of the system and prove its uniqueness. In the case of Ornstein-Uhlenbeck noise, we determine the speed of convergence to the invariant measure. Finally, we determine an approximate one-dimensional diffusion equation for the transition probabilities. The proofs use both spectral-theoretic and probabilistic methods.