量子散射理论中色散系统的时间延迟
Time delay for dispersive systems in quantum scattering theory
摘要：
本文考虑了量子散射对$\{H_0=h(P),H\}$的时滞和对称时滞（定义为逗留时间），其中$h(P)$为亚椭圆型色散算符.例如，$h(P)$可以是一个常用的椭圆算子，如薛定谔算子$h(P)=P^2$或平方根Klein-Gordon算子$h(P)=\sqrt{1+P^2}$。在一般条件下，我们证明了对称时滞对所有光滑偶局部化函数都存在。它等于Eisenbud-Wigner时间延迟加上由于局部化函数的非径向分量的贡献。如果散射算符$S$与速度算符$\nabla h(P)$的某个函数可交换，则时滞也存在，并且等于对称时滞。作为我们的结果的一个例子，我们考虑的情况下，一维的弗里德里希哈密顿量扰动的有限秩潜力。我们的研究证明了一个积分公式有关的微分算子相对于动能$h(P)$的时间演化的本地化运营商。
英文摘要：
We consider time delay and symmetrised time delay (defined in terms of sojourn times) for quantum scattering pairs $\{H_0=h(P),H\}$, where $h(P)$ a dispersive operator of hypoelliptic-type. For instance $h(P)$ can be one of the usual elliptic operators such as the Schrödinger operator $h(P)=P^2$ or the square-root Klein-Gordon operator $h(P)=\sqrt{1+P^2}$. We show under general conditions that the symmetrised time delay exists for all smooth even localization functions. It is equal to the Eisenbud-Wigner time delay plus a contribution due to the non-radial component of the localization function. If the scattering operator $S$ commutes with some function of the velocity operator $\nabla h(P)$, then the time delay also exists and is equal to the symmetrised time delay. As an illustration of our results we consider the case of a one-dimensionnal Friedrichs Hamiltonian perturbed by a finite rank potential. Our study put into evidence an integral formula relating the operator of differentiation with respect to the kinetic energy $h(P)$ to the time evolution of localization operators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
