Joan Simón

Variations of spread complexity

Krylov and Spread complexity have emerged as a powerful tool to quantify the growth of operators and states under time evolution. In this talk, we shall discuss the dependence of the spread complexity on the initial state, the hamiltonian and its dimension. The first appears naturally when asking whether spread complexity can diagnose quantum chaos, whereas the latter does when exploring the conditions leading to linear growth at long times. We propose a measure of coherence to diagnose quantum chaos in this context and explore its validity within motion in group manifolds. Time permitting, we shall discuss a solvable finite dimensional toy model, whose large N (continuum) limit leads to linear growth at long times. Interpreting the continuum model as an effective description for observers with finite resolutions, we observe the emergence of an effective 2nd law. The failure of the continuum model to reproduce the long time physics of the finite N model is interpreted this breaking down of the continuum model as an example of the breaking down of EFT due to large complexity considerations in more general physical setups.