Finding the Effective Dynamics to Make Rare Events Typical in Chaotic Maps.

Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise displaying unusual behavior. Yet, finding such initial conditions is a daunting task precisely because of the chaotic nature of the system. In this Letter, we circumvent this problem by proposing a framework for finding an effective topologically conjugate map whose typical trajectories correspond to atypical ones of the original map.

Spectral signatures of symmetry-breaking dynamical phase transitions.

Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. Some of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While macroscopic fluctuation theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging.

Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents.

The study of dynamical large deviations allows for a characterization of stationary states of lattice gas models out of equilibrium conditioned on averages of dynamical observables. The application of this framework to the two-dimensional random walk conditioned on partial currents reveals the existence of a dynamical phase transition between delocalized band dynamics and localized vortex dynamics. We present a numerical microscopic characterization of the phases involved and provide analytical insight based on the macroscopic fluctuation theory.

Symmetry-induced fluctuation relations in open quantum systems.

We derive a general scheme to obtain quantum fluctuation relations for dynamical observables in open quantum systems. For concreteness, we consider Markovian nonunitary dynamics that is unraveled in terms of quantum jump trajectories and exploit techniques from the theory of large deviations like the tilted ensemble and the Doob transform. Our results here generalize to open quantum system fluctuation relations previously obtained for classical Markovian systems and add to the vast literature on fluctuation relations in the quantum domain, but without resorting to the standard two-point measurement scheme.

Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks.

Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently in the presence of some obstacles or constraints. A somewhat related class of problems focuses on finding optimal distributions of weights which, for a given connection topology, maximize some kind of flow or minimize a given cost function. We show that both sets of problems can be approached through an analysis of the large-deviation functions of random walks.