2 problems

Let $d=1,2$, and let $u$ satisfy the bounds referred to in the source, with $2<\eta_2\leq\eta_1<4$, and suppose that $u(x)<0$ whenever $|x|>R$. Write $\zeta_c(\rho,\beta)$ for the…

Let $\rho>0$ be the particle density, $\beta>0$ the inverse temperature, and let $\rho$-dependent systems have one-particle eigenvalues…