5 problems

Let $e_{\rm 3B}$ denote the ground-state energy per unit volume in the thermodynamic limit, let $\rho$ be the particle density, and let $b_{\mathcal M}(V)$ be the three-body scatte…

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…

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

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…

Emergence of the renormalized Gibbs measure. In the limit $\lambda=T^{-1}\to0$, one obtains the renormalized Gibbs measure in the sense that