7 problems

Let $U\in\operatorname{U}(N)$ have non-degenerate spectrum, and consider the effective action $S(\gamma,U,Q)$ and its leading-order saddle-point expansion. Among its critical subma…

Let ${\cal M}_S={\cal M}_{(p,r)}$ be one of the critical submanifolds other than the isolated points $\{\pm\Sigma_3\}$, and let ${\cal M}_{\bar S}$ be its particle-hole dual. Write…

Let $U$ be a unitary matrix and let $\gamma\neq 1$, with genericity meaning that the matrix $\operatorname{diag}(\gamma U,U)$ is not degenerate. For integers $p$ and $r$, let…

Let $D4B1$ be a Hilbert space, and let $D4A2$ and $D4B7$ denote the classes of SN and SP maps, respectively. The set $D4A2\backslashD4B7$ consists of SN maps that are not SP. Non-S…

Let $D4B1$ be a Hilbert space, and consider non-SP SNTP maps on $D4B1$. Here, SNTP maps are Hermiticity-preserving and trace-preserving, while SP maps preserve positivity on the re…

Consider chaotic eigenstates of quantum maps on the torus with the nodal domains defined from the signs of their real position components. In the appropriate scaling limit, the bou…

Let $\Phi^t_H$ be an ergodic Hamiltonian flow on an energy shell $\mathcal{E}_E$, with quantum Hamiltonian $\hat H_\hbar$ and eigenstates $\psi_{\hbar,j}$ of energies…