Integrability-to-chaos transition through the Krylov approach for state evolution.

The complexity of quantum evolutions can be understood by examining their spread in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this spread [Balasubramanian et al., Phys.

Classical approach to equilibrium of out-of-time ordered correlators in mixed systems.

The out-of-time ordered correlator (OTOC) is a measure of scrambling of quantum information. Scrambling is intuitively considered to be a significant feature of chaotic systems, and thus, the OTOC is widely used as a measure of chaos. For short times exponential growth is related to the classical Lyapunov exponent, sometimes known as the butterfly effect.

Assessing the saturation of Krylov complexity as a measure of chaos.

Krylov complexity is a novel approach to study how an operator spreads over a specific basis. Recently, it has been stated that this quantity has a long-time saturation that depends on the amount of chaos in the system. Since this quantity not only depends on the Hamiltonian but also on the chosen operator, in this work we study the level of generality of this hypothesis by studying how the saturation value varies in the integrability to chaos transition when different operators are expanded.

Impact of chaos on precursors of quantum criticality.

Excited-state quantum phase transitions (ESQPTs) are critical phenomena that generate singularities in the spectrum of quantum systems. For systems with a classical counterpart, these phenomena have their origin in the classical limit when the separatrix of an unstable periodic orbit divides phase space into different regions. Using a semiclassical theory of wave propagation based on the manifolds of unstable periodic orbits, we describe the quantum states associated with an ESQPT for the quantum standard map: a paradigmatic example of a kicked quantum system.

Many-Body Localization and the Emergence of Quantum Darwinism.

Quantum Darwinism (QD) is the process responsible for the proliferation of redundant information in the environment of a quantum system that is being decohered. This enables independent observers to access separate environmental fragments and reach consensus about the system's state. In this work, we study the effect of disorder in the emergence of QD and find that a highly disordered environment is greatly beneficial for it.