10 problems

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

Spohn's central-limit conjecture. For every fixed $\alpha>0$, as $T\to\infty$ this rescaled path increment should converge in distribution to a centered three-dimensional Gaussian…

Conjecture on boundedness of $\mathcal I_0$. The set $\mathcal I_0$ is bounded; equivalently, $E(P)=E(0)+1$ for sufficiently large $P$.

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

Let $H(P)$ be the Fröhlich polaron Hamiltonian on the phonon Fock space at total momentum $P\in\mathbb R^3$, and define the energy-momentum relation by … Rotation invariance gives…

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

Let $E_\alpha(P)=\operatorname{inf\, spec}\,H_\alpha^P$ be the fiber ground-state energy at total momentum $P$, and define the effective mass $m$ by … Let $\psi^{\rm Pek}$ minimize…

Let $\mathord{\mathfrak h}_\alpha=-\Delta+V_\varphi(x)+\mathbb{N}$ be the Fröhlich Hamiltonian in strong-coupling units, let $e^{\rm Pek}$ be the Pekar energy, and let…

Let $\mathcal{H}$ be the Hilbert space of the model, let $G_{\infty}(k,t)$ be the infinite-time normalized characteristic function defined in the preceding framework, and let…

Spohn's conjecture. The strong-coupling behavior of the actual Polaron measures should be closely related to the behavior of the mean-field measures.