8 problems

Pekar's conjecture. The limit $g_0$ exists and satisfies

Let $H(\alpha)$ be the Fröhlich polaron Hamiltonian, and let $M(\alpha)$ denote the effective mass of the particle–field system, defined as the inverse of the second derivative at…

Let $\Gamma$ be a smooth curve that is a local deformation of a straight line, with curvature $\kappa$, and let $\alpha$ be the coupling strength in the leaky-wire Hamiltonian. Def…

Spohn's Pekar-process conjecture. As $\alpha\to\infty$, the suitably rescaled strong-coupling limit

Strong-coupling quasi-particle scaling conjecture. There exists a continuous function $f:[0,\infty)\to[0,\infty)$ such that $f(s)\to1$ as $s\to\infty$ and

Quantum correction conjecture. The same formula should hold when $\Omega=\mathbb{R}^3$ as $\alpha\to\infty$.

Let $\Gamma$ be otherwise smooth but have one angle equal to $\pi-\beta$, and let $\lambda_j$ be the $j$-th eigenvalue of the corresponding leaky star-graph Hamiltonian…

Let $\Gamma$ be a connected infinite $C^4$-smooth curve that is straight outside a compact set. Let $\mathcal{S}_{\Gamma,\alpha}(\lambda)$ be the on-shell scattering matrix of…