Energy migration, by which bound electron-hole pairs (i.e. singlet excitons) travel through an organic semiconductor before decaying, is at the heart of functioning optoelectronic devices such as solar cells. Designing materials with large singlet exciton diffusion lengths Ld would strongly benefit the efficiency of such devices. In this context, recent reports in highly ordered polymeric fibers and non-fullerene acceptor thin films of Ld largely exceeding the typical 10-20nm values call for a detailed microscopic picture going beyond the usual (hopping) models. Among others, a key missing ingredient in most modelling studies so far deals with the role of inter-molecular charge-transfer (CT) excitations. These have the potential to magnify the exciton dispersion at the band bottom or act as gateways for long-range energy migration, but could equally be detrimental to transport due to the formation of low-lying energy traps. In TECTESA, we aim at providing an in-depth mechanistic analysis of singlet exciton diffusion in organic molecular semiconductors in presence of CT configurations, highlighting namely their contrasting effects on the shape of the thermally accessible excitonic density of states and the coupling to the nuclear degrees of freedom. To reach this ambitious goal, we will: (i) develop and implement a universal transport formalism based on mixed classical-quantum non-adiabatic molecular dynamic simulations that explicitly accounts for CT excitations; (ii) explore how intermolecular CT configurations affect the nature and dynamics of singlet excitons in reduced models, through a broad range of physical situations (from superexchange to hybridization and trapping); and (iii) apply our newly developed approach to study energy migration in realistic, fully atomistic, models for N-heterotriangulene supramolecular fibers and non-fullerene Y6 molecular acceptors, where preliminary investigations seem to intimate the presence of low-lying CT pairs.

A serious open issue is that there is no widely accepted solution to the Quantum Gravity Problem. This results in paradoxes and clouds the study of many problems from the cosmology of the early Universe to unified theories of fundamental interactions that should incorporate both the Standard Model of Elementary Particles and Gravity. This proposal aims at attacking the old problems from a new vantage point and to achieve long-awaited breakthroughs. The potential reward is enormous as the project aims to shed light on the wide range of problems by exploring a new avenue provided by the first working example of a Higher Spin Gravity (HiSGRA). It will (A) attack the Quantum Gravity Problem and give new consistent theories that should significantly extend our understanding; (B) the underlying higher spin symmetry should govern a number of condensed matter systems and we expect to prove the recently discovered remarkable dualities relating them; (C) these symmetries are also related to extensions of Deformation Quantization, which should lead to new developments in pure mathematics and consolidate A+B. HiSGRA's, as rather simple models, can give keys to the puzzles of the early Universe with potentially observable effects in the near future, to the old paradoxes of black hole physics and to real-world processes of black hole scattering, which together with B applies HiSGRA to physics. This project is timely and feasible thanks to the recent ground-breaking results obtained by me and collaborators: (1) the very first example of a quantum consistent HiSGRA has been constructed and shown not to suffer from the UV-divergences that are at the core of the Quantum Gravity Problem; (2) the same theory was instrumental in attacking the dualities in three-dimensional conformal field theories that govern the physics of many second-order phase transitions; (3) it made new verifiable predictions for correlation functions, which is the very first solid prediction from HiSGRA

Because of their reduced dimensionality and symmetry, two-dimensional (2D) materials withstand physical phenomena that are very different from their 3D bulk counterparts. Beside graphene, other members of the same family of materials include metal dichalcogenides (MX2) and hexagonal boron nitride (h-BN). Remarkably, while single-layer graphene is a semimetal, 2D h-BN is an insulator and 2D MoS2 is a direct bandgap semiconductor. A new paradigm in materials science consists in piling up into vertical stacks single sheets of 2D materials with complementary electro-optical characteristics, thereby paving the way to the fabrication of ultrathin and flexible multilayer heterostructure devices. DEMONH aims at designing multilayer architectures based on 2D material building blocks with tunable electronic structure and optical properties that can be prepared by solution processing techniques. Among many others, this approach offers the unique advantage that the electrical and optical characteristics of the elementary 2D units can be tuned over a broad range by functionalization of their surface with properly designed conjugated organic molecules, which: (i) assist in the exfoliation process and stabilize single or multiple layers as suspensions in the liquid phase; and (ii) convey to the resulting hybrid organic-2D materials new or improved functionalities. In particular, the use of light-responsive molecules opens up the possibility to remotely switch on and off charge injection and extraction at interfaces. In DEMONH, we will combine state of the art modeling tools to design multifunctional electro-active conjugated molecules yielding optimized (light-triggered) energy level alignment at interfaces and charge transport properties in stacked 2D layer architectures. Such design strategies require the development of appropriate theoretical models and their coding in efficient software programs, which will be implemented in a multiscale modeling platform.

Low-rank matrix factorizations (LRMFs), such as principal component analysis, nonnegative matrix factorization and sparse component analysis, are linear dimensionality reduction techniques and are powerful unsupervised models to represent and analyze high-dimensional data sets. They are used in a wide variety of areas such as machine learning, signal processing, and data mining. Many LRMFs have been proposed in the literature, in particular in the last two decades, and used extensively in many applications, such as recommender systems, blind source separation, and text mining. Although LRMFs have known and still know tremendous success, they have several limitations. Two key limitations are that they are linear models, and that they only learn one layer of features. In this project, we go beyond LRMFs, considering generalized LRMFs (G-LRMFs) that overcome these limitations, considering non-linear and deep LRMFs. These generalizations have been introduced more recently, and they have hardly been explored compared to LRMFs. In particular, eLinoR will focus on three fundamental aspects: (1) Theory: understand G-LRMFs with a focus on computational complexity and identifiability (uniqueness of the decompositions), (2) Algorithms: solve G-LRMFs via provably correct and heuristic algorithms, and (3) Models: design new G-LRMFs for specific applications. This unified approach will enable us to understand these problems better, to develop and analyze algorithms, and to then use them for applications. The novelty and ground-breaking nature of this project also lies in the methodology, exploring G-LRMFs from different but complementary perspectives, bringing together ideas from different fields. The ultimate goal of eLinoR is to provide practitioners with theoretical and algorithmic tools for G-LRMFs, allowing them to decide which model and algorithm to use in which situation and what kind of outcome to expect, leading to a widespread and reliable use of G-LRMFs.