12 problems

Zeno product formula conjecture. If assumption in Theorem II.6a is dropped, then for every $f\in{\mathfrak h}$, $T>0$, and arbitrary admissible function $\phi$,

Let $\opL$ be an irreducible object with associated set $\Lambda_\opL$, preorder $\preceq$, period $N_\alpha$, and invariant $\varsigma_\alpha$ for each $\alpha\in\Lambda_\opL$. Ma…

Let $\eqp$ be an irreducible ergodic quantum process, and let $\GammaGroup$ denote its periodicity group. Cyclicity conjecture. The group $\GammaGroup$ is cyclic. The group is fini…

Let $\eqp$ be an irreducible ergodic quantum process defined by $\seq{\theta, \phi}$, and let $\alpha\in\PerSpecEQP$. For the disordered quantum process defined by…

Uniqueness conjecture. The Schrödinger algebra $\mathcal{S}$ admits a unique faithful realization as a subalgebra of $\hat{A}_1$, up to automorphism. This realization is the one ex…

Let $H(t)$ be a time-dependent Hamiltonian with period $1$, let $U(0,t)$ be its time-evolution operator, and let $|\psi(t)\rangle=U(0,t)|\psi(0)\rangle$ be the state evolved from a…

Nonlinear majorization monotone conjecture. If there exists a blockwise bistochastic matrix $\bm{B}\in\mathcal{B}_{n,d}$ such that $\bm{Q}=\bm{B}\*\bm{P}$, then for any ordering of…

The preceding theorem concerns a collection of generators for controlled Markovian quantum dynamics, with the relevant notation and generator class defined there. Converse characte…

Let the $(M,L)$-partitioned Hamiltonians be the Hamiltonians referred to as … have a spectrum. In the leading-order approximation, the partitioned-Hamiltonian unitarity conjecture.…

Analytic-root conjecture. Each root of $P(t,z)$ is an analytic function of $t$ with period $1$.

Ornstein–Uhlenbeck scaling-limit conjecture. As $\lambda\to0$, with convergence in law for the Skorokhod metric,

Freidlin–Wentzell/semi-classical limit. For $\lambda\ll 1$,