9 problems

Let a non-integrable quantum system be given, and let the strong eigenstate thermalization hypothesis (strong ETH) denote the property corresponding to Lemma 4 for the system's coa…

Consider the general ETH matrix model with higher-order coupling functions $G^{(n)}(E_a,\ldots,E_n)$ chosen by matching its correlation functions to the disk-level gravity predicti…

The ETH ensemble is a matrix model whose couplings and density of states are chosen to match the physical disk-level correlators, including the higher moments…

Let chaotic quantum eigenstates be expressed in a generic basis, and consider their overlaps with the basis vectors. Berry's conjecture. These overlaps can be thought of as random…

Let an extended many-body quantum system satisfy the eigenstate thermalization hypothesis (ETH), and consider quantum trajectories generated by monitoring a sufficiently large set…

Optimal convergence-rate conjecture. We conjecture that

Eigenstate Thermalization Hypothesis. The local statistics of the off-diagonal matrix elements satisfy

Eigenstate Thermalization Hypothesis. The diagonal expectation values satisfy

Let $E_{\alpha}$ and $\Psi(\alpha)$ be exact eigenvalues and eigenfunctions of the full $N$-particle Hamiltonian. For a finite system, let $E_0$ be the mean energy of the initial s…