论文标题
散射理论中渐近完整性的通用性质
Generic nature of asymptotic completeness in dissipative scattering theory
论文作者
论文摘要
我们回顾了在耗散量子系统的散射理论中获得的最新结果，这些量子系统代表了与另一个系统$ s $交互的系统$ s $的长期演变，并且容易被$ s'$吸收。 $ s $的有效动力学是由$ h = h_0 + v - \ mathrm {i} c^* c $的运算符生成的，$ s $的希尔伯特空间上，其中$ h_0 $是$ s $，$ v $ symmetric和$ c $的自由动力学的自动化动力学。主要的例子是与核光学模型中的核相互作用的中子。我们回想起对$ $（H，H_0）$的散射理论的基本对象，以及在Arxiv中证明的结果：1703.09018和Arxiv：1808.09179，涉及$ H $的光谱奇异性以及波浪操作员的渐进性。接下来，对于核光学模型，我们表明渐近完整性一般存在。
We review recent results obtained in the scattering theory of dissipative quantum systems representing the long-time evolution of a system $S$ interacting with another system $S'$ and susceptible of being absorbed by $S'$. The effective dynamics of $S$ is generated by an operator of the form $H = H_0 + V - \mathrm{i} C^* C$ on the Hilbert space of the pure states of $S$, where $H_0$ is the self-adjoint generator of the free dynamics of $S$, $V$ is symmetric and $C$ is bounded. The main example is a neutron interacting with a nucleus in the nuclear optical model. We recall the basic objects of the scattering theory for the pair $(H,H_0)$, as well as the results, proven in arXiv:1703.09018 and arXiv:1808.09179, on the spectral singularities of $H$ and the asymptotic completeness of the wave operators. Next, for the nuclear optical model, we show that asymptotic completeness generically holds.
