3 problems

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

Let $H^{Bog}_{\bold{j}_*}$ be the Bogoliubov Hamiltonian restricted to the $N$-particle Fock space $\mathcal{F}^N$, and let $\Omega$ denote the vacuum vector. Define the normalized…

Let $E(N,Z)$ be the quantum ground-state energy and $E^{\rm B}(N,Z)$ the Bogoliubov ground-state energy. Let $e(t)$ and $\mu(t)$ be the leading and first-correction coefficients in…