This project addresses the effects of thermal particles on the condensate phase for bosons, focusing on systems with long-range interactions at finite temperatures. We explore ultra-light bosonic particles as dark matter candidates in cosmology and extend the study to cold atomic systems under dipolar interactions. Our approach involves a recently developed theoretical framework using non-equilibrium quantum field theory to describe two-component bosonic systems, condensed and thermal, under long-range interactions. We will create a specialized simulation code to study the dynamics of condensate and thermal particles in both cosmological and atomic contexts. This code aims to fill critical gaps in current research and will be made publicly available with detailed documentation. The project will involve two main objectives: (1) developing and validating this code, and (2) investigating pivotal problems in the dynamics of dipolar and cosmological quantum gases. By comparing results with existing methods and exploring new phenomena, this research seeks to provide significant advancements and uncover valuable analogies between ultracold atom and dark matter studies.

Artificial intelligence (AI) offers novel methodologies to unravel complex physical phenomena. However, most machine learning models lack transparency in their decision-making processes. In this proposal, we aim to develop a symbolic AI as a tool to reveal hidden topological orders in quantum physics. To this end, an AI-assisted symbolic regression method will be studied. We focus on three main objectives: (i) machine learning topological phases with experimental data; (ii) uncovering hidden non-local symmetry-protected topological orders; and (iii) searching for quantized topological invariants in an unsupervised fashion. The interplay between symbolic AI and quantum physics is envisioned to bring new insights into topological phases. Moreover, the project will scrutinize the explainability and the robustness of machine learning models. The investigations will provide concrete guidelines for accompanying theoretical and experimental studies at MagTop. The outcomes of the project will pave the way to discover novel features of topological materials in a reliable and explainable way, as well as provide great opportunities for me to reach a position of professional excellence and independence.

I will explore superlattices and heterostructures in chalcogenide materials as a platform for Berry-curvature engineering and topological devices. To this end, I will study superlattices created by superimposing single- and bilayers of transition-metal dichalcogenides with periodic arrays of magnetic adatoms in various configurations. Moreover, I will study multilayer heterostructures of group-II monochalcogenides with a compositional gradient across layers. The interplay of the underlying electronic structures with the ingredients and configurations of the superstructures is envisioned to lead to new phases with highly altered properties. I will study this interplay theoretically with a focus on three main objectives: (i) designing quantum anomalous Hall phases with large Chern numbers, which is highly relevant for electronic devices with low-power consumption; (ii) realizing topological superconductors as a platform for Majorana quasiparticles, which hold potential for exotic nonlocal phenomena and quantum computers; and (iii) realizing stable intertwined order in a 3D material with flat energy bands, a research direction I will pioneer with this project. I will model the proposed setups numerically using low-energy tight-binding models of the materials. The models will be constructed in close collaboration with experimentalists and DFT experts at the host institution MagTop within IF PAN. I will calculate Berry curvature, topological invariants, magnetic order, phase diagrams, and signatures of the emerging phases with regard to charge, spin, and thermal transport. The code used for the calculation of these quantities will be implemented as a software package, which I will utilize and develop during this project. My investigations will provide concrete guidelines for accompanying experimental studies at MagTop. In this way, the outcomes of my project will lay the foundation for tunable topological devices based on chalcogenide superlattices and heterostructures.