Conclusions

For the reader’s convenience, we summarize the main speed limits derived in this thesis. The goal of this thesis was to characterize the time evolution of isolated quantumsystems by providing universal constraints on their dynamics and on the resulting buildup of quantum complexity. As argued in the introduction, in order to capture the complex behavior of many-body systems, the most suitable representation of the dynamics is the Heisenberg one, in which it is the observables of the system that evolve in time. In this work, we have constrained the operator growth by (i) formulating the so-called dispersion bound [1] on the rate of Krylov complexity and (ii) extending the paradigm of QSLs to operator flows [2, 3].