14 problems

Consider a quantum many-body system initially prepared in the ground state of one Hamiltonian and subjected to a sudden change of interaction strength, or quench. Local relaxation…

Let $\mathcal{G}$ be an infinite, irreducible, bounded-degree graph, let $\nu_{L,o}$ denote the $L$-step heat-kernel measure rooted at $o$, and let $\partial A$ be the boundary of…

Let ${\sf Dyn}$ be a constrained dynamics and let $\mathcal{G}_{\mathcal{K}}$ be its Krylov graph. Suppose that ${\sf Dyn}$ is exponentially fragmented. Krylov-graph shattering con…

Let $\mathcal{H}$ be the system Hilbert space and let $\mathcal{K}_{\max}$ be its largest Krylov sector. Dynamics is exponentially fragmented when … Consider depolarizing noise act…

Non-integrability conjecture. Any $\hat{V}$ that makes the total Hamiltonian $\hat{H}_L+\lambda\hat{V}$ non-integrable will lead to thermalization of the time-evolved state for suf…

Conserved charges are observables whose expectation values are preserved by the dynamics of a quantum system. A collection of conserved charges is non-commutative when its members…

Consider random quantum circuits modeling quantum chaotic dynamics and possessing a conserved quantity. Entanglement-thermalization conjecture. Entanglement thermalizes in random q…

Slow-thermalization conjecture. Starting from the uniform measure, Langevin dynamics takes exponential time to reach equilibrium for every $T<T_{sh}$: there is a constant $c>0$ suc…

Let $h=1/n$ be the small lattice-spacing parameter for the Fermi–Pasta–Ulam–Tsingou chain, let $E$ denote its total energy, and let $E/n$ be the specific energy. The asymptotic int…

Universal thermalization conjecture. Within this harmonic-potential, white-noise setting, the SLE universally leads to thermal equilibrium of statistical mechanics.

The Fermi–Pasta–Ulam chain has $N$ identical masses connected by nonlinear springs, with the elastic force expanded as … The original $\alpha$-FPU system is the case $\alpha\ne0$ a…

Thermalization conjecture.

Eigenstate thermalization hypothesis. There are no eigenstate-to-eigenstate fluctuations in the diagonal matrix elements $A_{\alpha,\alpha}$ for eigenstates close in energy; equiva…

Let an isolated macroscopic system be chaotic in the classical limit, and consider a single eigenstate of its Hamiltonian. Single-eigenstate Boltzmann–Gibbs conjecture. Even a sing…