This project aims to study topological and dynamical aspects of two dimensional paradigm of chaos called Hénon attractors and introduce new treatable parametrised family of strange attractors appearing in smooth dynamical systems. Despite Hénon attractors have been known to mathematicians for more than 40 years, the topology of the attractors has not been studied in details yet. The main obstacle that such a study has not been established was the lack of techniques necessary to perform it. Building on recent advances in describing parametrised families of strange attractors using inverse limits we will delve in such a detailed study and give new results on topological, dynamical and measure-theoretic features appearing in parametrised families of strange attractors. We will use methods and techniques from Topological, Smooth, Surface and Symbolic Dynamics as well as Continuum and Ergodic Theory.

Classical thermodynamics is a long-standing successful theory using macroscopic average quantities like pressure, volume, and temperature to describe the behaviour of everyday thermal machines. In nanophysics, it is often the case that fluctuations can become dominant over average quantities, which are therefore no longer sufficient for an accurate description of nanoscale and quantum systems. Advances in nanoelectronics have allowed researchers to engineer devices that can turn fluctuations from a nuisance into a resource to power nanoscale quantum machines. However, many questions on these fluctuation harvesting mechanisms are still open. With the theoretical project FLUTE, I will address these questions by investigating the impact of fluctuations on the performance of quantum thermal machines in nano-electronic conductors powered by unconventional resources and exhibiting topological properties. Specifically, I will consider nonthermal resources and exotic quasiparticles, called anyons, hosted in two-dimensional conductors. FLUTE seeks to generate a deeper understanding and provide novel insights on how the efficient harvesting of fluctuations at the nanoscale can be achieved. Crucially, it will bring together in a novel way the physics of anyons found in condensed matter systems with a thermodynamical analysis aimed at exploiting them as fuel for useful machines. This interdisciplinary project will combine techniques from quantum transport and strongly correlated systems, on which I am an expert, to stochastic thermodynamics and open quantum systems, on which I will receive further specific training at the host institution. FLUTE will unveil novel connections between different research fields in quantum physics. The outcomes of the project will be relevant for the design of novel types of quantum devices exploiting unconventional resources, thus contributing to the emerging field of quantum technologies, driven at the European level by the Quantum Flagship.