18 problems

Fix an integer $N$. For a periodic box of size $L$, let $E_L^N(\varphi)$ be the Hartree–Fock minimum in the charge sector with trace $N$, let $E_L(0)$ be the corresponding vacuum e…

Bounded-boundary-variation conjecture. Only boundary conditions for which the variation of the function $\phi$ along the boundary remains bounded will lead to the usual thermodynam…

Uniqueness conjecture. The state $\omega_{\mathbb{Z}^D}^\beta$ obtained in this way is the only thermodynamic-limit $\beta$-KMS state.

Let $e_{\rm 3B}$ denote the ground-state energy per unit volume in the thermodynamic limit, let $\rho$ be the particle density, and let $b_{\mathcal M}(V)$ be the three-body scatte…

Let $V$ be the total volume, let $A$ be a subsystem of volume $V_A$ with fraction $f=V_A/V$, and let $\braket{\Delta C_A}_G$ denote the standard deviation of the eigenstate capacit…

Consider the non-compact Fermi distribution of the XXX model in zero external field, and spectral parameters lying in the bulk of the Fermi distribution. The condensation property…

Consider the $SL(2,\mathbb{C})$ non-compact spin chain of length $L$, and let its ground-state energy be the lowest energy among its states. Thermodynamic vanishing conjecture. The…

Fix the ratio $n/N$, where $n$ is the number of Bethe roots and $N$ is the system size, and let $C$ denote the contour described in the paper. Thermodynamic Bethe-root contour conj…

Let $d\geqslant 1$ and $-2\leqslant s<d$. Consider the Jellium model in $d$ dimensions with Riesz interaction and define its lowest energy in a background region $\Omega_N$ of volu…

Effective-series thermodynamic-limit conjecture.

Thermodynamic-limit conjecture. The specialization $\rho_{N;\mathrm{eff}}(x,t\mid\gamma=1)=\rho_{N;\mathrm{eff}}(x,t)$ has the same thermodynamic limit as $\rho_N(x,t)$.

Consider a random loop configuration in a box $\Lambda$ of side length $L$, with loop lengths $\ell_j(\omega)$ ordered decreasingly. Let $m(\beta)$ denote the limiting density of p…

Let $\rho_{\infty}^{t}$ be the infinite-volume time-evolved state and let $V_{n}$ be the vertex set at volume $n$. Along a subsequence $\{m_{n}\}$, suppose the transverse magnetiza…

Let $H^L$ be the finite-volume Hamiltonian of an interacting Fermi gas in a periodic box, with ground-state energy $E^L$. For momentum ${\bf k}$, let $\epsilon^\pm({\bf k})$ denote…

Let $\rho_N(x,t)$ be the finite-volume reduced density matrix. Set ${\mathcal B}_L=\{n\in\mathbb Z:-w_L<n<w_L\}$,…

Let $\rho_N(x,t)$ be the finite-volume reduced density matrix, let $\rho_{N;\mathrm{eff}}(x,t)$ be the effective reduced density matrix obtained by retaining the prescribed low-ene…

Let $L$ and $N$ tend to infinity together, and let ${\mathcal{Q}}_N^\kappa(x,t)$ denote the original finite-size series for the current-current correlator. Let…

Bistable-regime conjecture. The measure $(u_0\cdot\lambda)^{\mathbb N}$ is not charged in the limit.