5 problems

Excitation-spectrum conjecture. The low-lying spectrum of $H_N^{\rm GP}$ is given by

Barrier-removal conjecture. The barrier can be removed, so that Theorem holds in the larger Region $\mathrm{III}^{\prime}$.

Let $H_N^{\rm Comb}$ be the Hamiltonian with two-body potential $W$ at scaling parameter $\beta=1$ and three-body potential $V$. Let $e^{\rm Comb}_{\rm GP}(b_1,b_2)$ be the minimum…

Let $H_N^{\rm GP}$ be the Gross–Pitaevskii Hamiltonian, let $E_{\rm GP}(N)$ denote its ground-state energy, and let $e_{\rm GP}$ be the minimum of the corresponding Gross–Pitaevski…

In the NLS and Gross--Pitaevskii scaling regimes, the interaction scales as $N^{-1+3\beta}v(N^{\beta}x)$ for $0<\beta\leq 1$ in three dimensions, and the correlations are larger be…