QSLs on Correlation Functions

Correlation functions between quantum operators at different times represent a prominent tool to investigate the dynamics of many-body quantum systems. In particular, they characterize the response of a system to an external perturbation. In addition, they account for the buildup of complexity through operator growth. In this chapter, we recast our OQSLs on operator flows as bounds on equilibrium autocorrelation functions and assess a universal crossover between a MT and a ML regime, which we illustrate in a qubit system and in a random matrix model [1]. We further provide three different constraints on the dynamical susceptibilities that characterize the transport properties of many-body systems and give concrete examples in the case of electric and magnetic transport [1]. Finally, from a ML QSL on correlation functions, we derive an upper bound [1] on the thermal Fisher information, thus enlightening a new connection between the framework of QSLs and quantum metrology.