14 problems

Transport-distance finiteness conjecture. If $\Phi$ is $(p+\vartheta)$-uniform for some $\vartheta>0$, then

Consider an integrable many-body system in a no-shock regime with ballistic scaling $\mathrm{x}=\ell x$ and $\micro t=\ell t$ as $\ell\to\infty$. Let $\xi$ denote the fluctuating-h…

Let $\bar n$ denote the particle density, and consider an operator evolving in a many-body system at low density. Let $Q=1$ denote the single-particle sector of the Hilbert space.…

Mazur-bound saturation conjecture. If all the charges $A_j$ are known, then the Mazur bound saturates. This conjecture asserts that a complete set of quasilocal charges accounts fo…

For the one-dimensional Stark operator ${{\mathcal S}}_a$ on $L^2({\mathbb R})$, with $a\in{\mathbb R}\setminus\{0\}$ and … consider the weighted $L^2$-norm of the time evolution…

Let a trajectory of the ABC flow cross the boundary of a cell. Infinite-crossing conjecture. Almost all trajectories that cross the boundary of a cell will cross cell boundaries in…

In a one-dimensional lattice model, let momentum be conserved and consider the long-time, large-scale transport of energy. Momentum-conservation superdiffusivity conjecture. Moment…

Let the travelling potential be … where $\psi$ is $1$-periodic and $\omega$ is a constant. Consider the corresponding ratchet and denote its average drift velocity by $v$. Positive…

Let $D_J$ denote the thermodynamic high-temperature spin Drude weight, and let … be the lower-bound quantity at anisotropy $\eta=\pi l/m$, where $l$ and $m$ specify the correspondi…

Consider the disordered harmonic chain and the rotor chain in the absence of noise, $\boldsymbol{\varsigma}=0$, and let $\boldsymbol{\varepsilon}$ denote the coupling parameter. Ro…

Let $\boldsymbol{\kappa}_2(\boldsymbol{\varsigma})$ be the coefficient governing the weak-coupling conductivity, and let $\boldsymbol{\varsigma}$ be the velocity-flip noise paramet…

Let $\beta$ be the inverse temperature, $\boldsymbol{\varepsilon}$ the coupling parameter, $\boldsymbol{\varsigma}$ the noise parameter, $\boldsymbol{j}_{0,1}$ the local current, a…

Let $\beta$ be the inverse temperature, $u$ the resolvent parameter, $beta^{-2} obreaktext{}$ the normalization used for the conductivity, and let $boldsymbol{j}{0,1}$, $v{ u,1}$,…

Generic transport conjecture. Transverse intersections of stable and unstable manifolds of whiskered tori should be a generic mechanism for transport in phase space and global inst…