4 problems

Spin-1/2 Fermi energy conjecture. The ground-state energy is conjectured to have the expansion

Consider dilute one-dimensional spinless bosons and fermions, with energy expansions expressed in terms of their corresponding scattering lengths. Scattering-length universality co…

Let $N$ particles form a dilute one-dimensional spin-$1/2$ Fermi gas of density $\rho$, with even-wave and odd-wave scattering lengths $a_e$ and $a_o$, respectively. The free Fermi…

Overlap-asymptotics conjecture. The exponent $\gamma$ governs the true asymptotics of the overlap whenever the modulus of the appropriately defined scattering phases does not excee…