5 problems

Let $g_1(x,x')$ be the one-particle density matrix of the translation-invariant Tonks–Girardeau gas with uniform density $\rho$, and suppose that for $|x-x'|\gg\rho^{-1}$ it satisf…

Let $e(\gamma)$ denote the ground-state energy of the $\delta$-Bose gas at weak coupling, expanded in powers of $\gamma^{1/2}$, and let the coefficient of $\gamma^{1+m/2}$ be under…

Special-dimension conjecture. The formula $d_m=2+\frac{2}{m+1}$ holds for all $m=1,2,\ldots$. These dimensions are conjectured to explain exceptionally large convergence radii of t…

Let $\eta$ be the shear viscosity, $s$ the entropy density, $\hbar$ the reduced Planck constant, and $k_B$ Boltzmann's constant. Kovtun–Son–Starinets conjecture. The ratio of the s…

GGE applicability conjecture. The GGE is applicable to the 1D Bose gas (LL model), at least for local observables.