8 problems

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…

For integers $p\geq1$, define … These operators are type II Hamiltonians when the relevant $\ket{W^{p'}}$ states are exact scars for $p\leq p'$. Independent-Hamiltonians conjecture…

Let $\ket{W^p}$ be a $W^p$ droplet containing $p$ particles in an initial domain of size $M$, and let $\rho=p/M$. Low-density BEC conjecture. The treatment of the $W^p$ state as a…

Let an interacting type II Hamiltonian act on a $W$-state droplet, with its action localized at the droplet boundaries. Ballistic-motion and diffusive-melting conjecture. The inter…

Consider the spin-1 XY case on a chain of length $L$, with open boundary conditions (OBC) or periodic boundary conditions (PBC). Let $\ket{\Phi_n}$ denote the spin-1 XY QMBS tower…

Let $\mA^{\mathrm{FM}}_{\scar}$ be the local algebra associated with the ferromagnetic QMBS, and consider a properly extensive local Hamiltonian constructed from this algebra. The…

Let a local Hamiltonian have certain sets of quantum many-body scar (QMBS) states as eigenstates. Equally spaced towers conjecture. Certain sets of QMBS necessarily appear as equal…