6 problems

Let $\Gamma$ be an infinite asymptotically straight curve without self-intersections, with two leads. Suppose that the distance between points of $\Gamma$ becomes small somewhere,…

Consider the nonlinear Schrödinger evolution with perturbation $\eta|\psi_t|^2\psi_t$, where $\eta\in\mathbb R$, and let the associated quantum-resonance energy be $E$. The surviva…

Consider the nonlinear Schrödinger evolution with perturbation $\eta|\psi_t|^2\psi_t$, where $\eta\in\mathbb R$ is the nonlinearity strength, and let $\tilde\eta$ be the negative t…

Let ${\mathcal A}(t)=\langle\psi_0,\psi_t\rangle$ be the survival amplitude and ${\mathcal P}(t)=|{\mathcal A}(t)|^2$ the survival probability. In the regime where quantum-resonanc…

Let $Z_{GV}(k)$ be the Gutzwiller–Voros zeta function, defined through the transfer-operator Fredholm determinants by … Here $k$ is the semiclassical spectral parameter, and the qu…

Consider an $n$-disk scattering system and its semiclassical zeta function, whose zeros are complex spectral parameters associated with the classical dynamics, together with the qu…