A resonance theory for open quantum systems with time-dependent dynamics

Resonance Theory for Schroedinger Operators

Resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods. A general theory is developed, with new and weaker conditions, allowing for perturbations of threshold eigenvalues and relaxed Fermi Golden rule. The exponential decay rate of resonances is addressed; its uniqueness in the time dependent picture is shown is certain cases. The relation to the existence of meromorphic continuation of the properly weighted Green's function to time dependent resonance is further elucidated, by giving an equivalent time dependent asymptotic expansion of the solu…

Resonances in Models of Spin Dependent Point Interactions

In dimension $d=1,2,3$ we define a family of two-channel Hamiltonians obtained as point perturbations of the generator of the free decoupled dynamics. Within the family we choose two Hamiltonians, $\hat H_0$ and $\hat H_\ve$, giving rise respectively to the unperturbed and to the perturbed evolution. The Hamiltonian $\hat H_0$ does not couple the channels and has an eigenvalue embedded in the continuous spectrum. The Hamiltonian $\hat H_\ve$ is a small perturbation, in resolvent sense, of $\hat H_0$ and exhibits a small coupling between the channels. We take advantage of the complete solvabili…

半直线上能量依赖势的共振与逆问题

Resonances and inverse problems for energy-dependent potentials on the half-line

本文研究了半直线上紧支撑且线性能量依赖势的薛定谔方程，给出了特征值与共振数目的估计，解决了无特征值情况下的逆共振问题，并利用薛定谔与Dirac方程的对应关系简化了散射问题。