论文标题
量子图的粒子轨迹
Particle Trajectories for Quantum Maps
论文作者
论文摘要
我们在量化的圆环的环境中研究了克劳斯操作员重复间接测量的半经典量子粒子的轨迹。在两次测量之间，系统通过哈密顿繁殖器或元容器进行演变。在这两种情况下，我们都显示了量子轨迹与其相应的经典轨迹的总变化，这是通过半经典缺陷度量的传播定义的。这种收敛性可容纳经典系统的Ehrenfest时间，当系统较少时，该系统较大。此外，我们提出了这些影响的数值模拟。 在证明这一结果时，我们提供了一种半古典缺陷度量的表征，我们称之为统一的缺陷度量。我们还证明了由圆环上的流动组成的函数的导数估计。
We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or metaplectic operators. We show in both cases the convergence in total variation of the quantum trajectory to its corresponding classical trajectory, as defined by propagation of a semiclassical defect measure. This convergence holds up to the Ehrenfest time of the classical system, which is larger when the system is less chaotic. In addition, we present numerical simulations of these effects. In proving this result, we provide a characterization of a type of semi-classical defect measure we call uniform defect measures. We also prove derivative estimates of a function composed with a flow on the torus.
