Eigenstate thermalization and integrability breaking

4 problems

• Does the relaxation rate scale as $g^{2}$ in the thermodynamic limit

  Open

  Simple theory says a weak perturbation of strength g makes a solvable system relax at a rate proportional to g squared. The question is whether this holds exactly for very large systems or whether the rate is parametrically smaller.

• Thermalization speed with noncommuting conserved charges

  Open

  Standard thermalization theory assumes all conserved quantities (energy, particle number) can be measured at once. When some cannot, for example the three components of total spin, it is unclear whether thermalization works the same way and at the same speed.

• Energy scale below which ETH matrix elements become random-matrix-like

  Open

  ETH says the table of a local observable between energy eigenstates looks random, but only for eigenstates very close in energy. How wide that energy window is, and how it shrinks with system size, is not settled.

• How thermalization sets in when integrability is weakly broken

  Open

  When a solvable chain of interacting spins is perturbed slightly, it should eventually thermalize, but how long that takes and through which intermediate states is unclear. Small-system numerics often show slower relaxation than simple perturbation theory predicts.