In the proposed project "Entanglement-Assisted Thermoelectric Transport in Quantum Systems" (EATTS), the European Researcher Dr. Nahual Sobrino, together with Prof. Rosario Fazio at the International Centre for Theoretical Physics (ICTP), will collaborate with international research groups to unveil innovative thermoelectric properties that hold transformative potential for sustainable energy technologies, quantum information science, and the development of advanced quantum materials. The project's objectives will concentrate on the exploration of thermoelectric phenomena mediated by entangled electrons across a variety of quantum systems. A comprehensive theoretical and computational framework will be established to explore and enhance thermoelectric performance in systems where electron entanglement plays a pivotal role. Cutting-edge calculations will be performed using sophisticated theoretical frameworks, including Quantum Master Equations (QME), Hierarchical Equation of Motion (HEOM), and quantum information techniques. This will guide to elucidate the intricate relationship between entanglement, system-environment interactions, and thermoelectric performance in Double Quantum Dots (DQD) and Cooper Pair Splitters (CPS) systems. Moreover, the project aims to extend the scope of Density Functional Theory (DFT) to access to entanglement measures in transport scenarios through the development of extensions of iq-DFT. This will facilitate a more efficient computational description of thermoelectric phenomena under the influence of entangled electrons. Additionally, the thermoelectric and entanglement characteristics of multiple diatomic molecules will be investigated by mapping the system into effective Hamiltonian models. The computational framework developed will advance our understanding and serve as a guide for experimental endeavors by selecting promising materials and parameter regimes.

WaveNets aims to establish a novel theoretical paradigm for understanding quantum systems, centred on a network interpretation of many-body wave-functions. Ongoing experimental progress motivates the need for a new theoretical approach: in the field of quantum simulation and quantum computing, probing capabilities have reached unprecedented levels, with the ability to collect thousands of wave function snapshots with impressive accuracy. However, most of our theoretical understanding of such settings still relies on and relates to few-body observables. This has created a clear gap between experimental capabilities and theoretical tools and concepts available to understand physical phenomena. The overall goal of WaveNets is to bridge this gap by introducing a mathematical framework to describe wave-function snapshots based on network theory — wave function networks — that will enable a completely new set of tools to address open problems in the field of quantum matter. WaveNets' main objectives are: - to demonstrate that wave function snapshots of correlated systems are described by scale-free networks, and classify the robustness of quantum simulators according to such; - to formulate methods for quantifying the Kolmogorov complexity of many-body systems, and propose an information-theory-based characterization of topological matter and confinement in gauge theories; - to propose scalable methods for measuring entanglement in quantum simulators and computers, as well as for their validation. Achieving these objectives will (a) provide unique insights into the information structure of quantum matter, (b) enable methods of probing and controlling matter of direct experimental relevance thanks to the intrinsic scalability of network-type descriptions, and (c) establish a new, interdisciplinary bridge between quantum science, and network and data mining theory, that makes possible knowledge transfer between two mature, yet poorly connected disciplines.

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.