7 problems

Large-coupling absence conjecture. There exists $\lambda_{\mathsf c}>0$ such that $H(\lambda,0)$ has no ground state for

Consider the two-dimensional Ising model on the periodic torus … with nearest-neighbor ferromagnetic coupling $J$, Hamiltonian $\mathcal H_L$, periodic striped configurations…

For $d=2$, let $Q_\omega$ denote a cubic-quintic ground state solution at frequency $\omega\in(0,\tfrac{3}{16})$. Orbital stability conjecture. All cubic-quintic ground state solut…

Let $H_{\Lambda,J}$ be the finite-volume Hamiltonian in a box $\Lambda$ with $|\Lambda|=L^d$, and let $\sigma^1$ and $\sigma^2$ be chosen as in Theorem. Write $\operatorname{Var}$…

Let $\Phi_0$ and $\Phi_1$ be two translation-invariant finite-range interactions. For $i=0,1$, suppose there are integers $l_i$ and $r_i$ such that … Here ${\mathcal S}_i^\Gamma$ d…

Ground-state domination conjecture. Then $\lambda$ belongs to the spectrum of the Friedrichs extension of $P$ on $L^2(\Omega,\mathrm{d}x)$. This conjecture links pointwise dominati…

High-density ground-state and infinite-density ground-state conjecture. If $u$ is superstable and strongly tempered, then high-density GSCs and IDGSs in infinite space exist. Every…