4 problems

Let $n$ bosonic particles have relativistic kinetic energy, and let $\mathcal{H}_{V\equiv 0}$ denote the pseudo-relativistic Hartree energy functional with vanishing external poten…

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…

Semiclassical mean-field limit conjecture. For every function $f$ satisfying $f\geqslant 0$, $\sqrt{f}\in H^1(\mathbb{R}^d)$ and $\int_{\mathbb{R}^d}f=1$, one has

Let $\beta=1$ be the critical scaling. Suppose that $\phi$ and $k$ satisfy the equations of Theorem, and let $\big\vert\psi_{exact}\big>$ and $\big\vert\psi_{appr}\big>$ be the exa…