99 problems

Consider a power-law interacting system on a $d$-dimensional lattice, with exponent $\alpha$, and the transition from an algebraic to a linear Frobenius light cone. Critical-expone…

Optimal uniform-rate conjecture. At least for the linear case, the optimal uniform-in-$h$ convergence rate should be $\Delta t^2$.

Let $v(t)$ denote the evolution speed of a state under open quantum dynamics, and let the speed of relative purity change be bounded using the Cauchy–Schwarz inequality. Monotonici…

Genuine nonlinear quantum-map conjecture. If Newtonian dynamics is more general than Hamiltonian dynamics, then genuine nonlinear quantum maps should exist, and nonlinear Schröding…

Quantum-chaos shadow conjecture. Quantum mechanics suppresses chaotic behavior so that only some “shadows” of chaos can remain.

Quantum-chaos suppression conjecture. Quantum mechanics suppresses chaotic behavior so that only “fingerprints” of chaos can remain.

Asymptotic-Hamiltonian conjecture. The Hamiltonian $H_{{\rm S},\lambda,\beta}$ absorbs the leading-order correction to the non-interacting dynamics

Consider a multistate Landau–Zener model in which the diabatic energies depend linearly on time. A transition is counterintuitive when it goes against the ordering implied by the d…

The piecewise deterministic process is defined on the non-compact Poincaré disk, with quantum jumps having place-dependent probabilities and dissipative continuous evolution over r…

Let $y:\mathbb{R}\to\mathbb{R}^3$ be a curve and let $H_{\alpha,y}(t)=H_{\alpha,y(t)}$ be the corresponding time-dependent Hamiltonian, with quadratic-form domain $D(F_y(t))$ and p…

Let $H_0$ be a Hamiltonian with eigenvalues $\alpha_n$ of the form … Suppose that $\beta_jT/(2\pi)$ is Diophantine for some $j$ with $1\leq j\leq p$, and let $V_\lambda$ be the cor…

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 $\phi$,

For the random dimer model, let $\delta_1$ denote the initial state at site $1$, let $\beta_{\delta_1,\omega}^-(2)$ be its lower transport exponent of order $2$ for a realization…

Propagation of quantum molecular chaos conjecture. The sequence of Heisenberg maps $\phi_{n,t}(A)=e^{iH_nt/\hbar}Ae^{-iH_nt/\hbar}$ propagates chaos: if $\{\rho_n\}$ is $\rho$-chao…

Let $\beta(\alpha)$ denote the exponent governing the decay of the return probability, and let $D_1$ and $D_0$ denote, respectively, the information dimension of the relevant spect…

Consider a periodically driven two-level system with effective Hamiltonian expanded perturbatively in the driving frequency, whose leading terms involve the Pauli matrices…

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…

Matrix-algebra generation conjecture. If the jump operators $\{L_j\}_j$ generate the entire complex matrix algebra, then the associated dissipator is Hamiltonian-independently cont…

Consider fermionic cellular automata whose local algebras have larger dimension than those in the one-dimensional spinless model studied in the paper. Higher-dimensional local-alge…

Let an FDFC on $\mathbb Z$ have a renormalisation of the form $(N,\Pi_{\Lambda_0})$, where $N$ is even. A Majorana-shift renormalisation is a renormalisation to a Majorana shift. M…

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 a $W^p$ droplet have particle density $\rho=p/M$ in its initial domain, and compare its dynamics under extensive-local interacting quantum many-body scar Hamiltonians of type I…

Consider a $W$-state droplet evolving under a general type II Hamiltonian, and let the droplet domain remain intact up to its melting time. Boundary-driven directional-motion conje…