11 problems

Guha et al.'s entropy photon number inequality. The inequality

Let $I=[1,\ldots,m]^{\times D}$ be a cubic region in a $D$-dimensional lattice, and let $E_I^S$ denote its geometric entropy. For the interaction matrix with off-diagonal entries…

Collective-field approximation conjecture. For the more general problems considered in this paper, $F_{\phi}(v)$ is close to $F_\infty(v)$.

Let $G$ be a symmetry group and let $\cE=\operatorname{Rep}(G)$. A modular extension $\cM$ of $\cE$ is a UMTC containing $\cE$ fully faithfully and satisfying the defining centrali…

Let $g(N)=(N+1)\ln(N+1)-N\ln N$ be the entropy of a single-mode thermal state with mean photon number $N$, and let $N(\rho)=g^{-1}(S(\rho)/n)$ denote the mean photon number per mod…

A Bosonic linear channel is a channel of the form $\Phi_{K,f}$, with Heisenberg action $\Phi_{K,f}^*(W_B(z))=W_A(Kz)f(z)$ on Weyl operators. A Bosonic unitary dilation is a represe…

Consider bosons interacting through pair potentials, and suppose that the two-boson subsystem has a zero-energy resonance and no negative-energy bound states. Universal three- and…

Consider the generalized channels obtained by replacing the two-dimensional one-particle space ${\mathord{\cal H}}_{1/2}$ in the bosonic many-particle construction by an arbitrary…

Monotonicity conjecture. The map $N\mapsto\Lambda_*(N)$ is monotonically increasing.

Monotonic binding conjecture. A proper $N$-body ground-state wave function $\Psi^{(Z,N)}_{\mathrm{Bose}}$ exists for every integer $N$ satisfying

Threshold conjecture. A proper $N$-body ground-state wave function $\Psi^{(Z,N)}_{\mathrm{Bose}}$ exists whenever $Z>Z_*(N)$.