@phdthesis{10759, abstract = {In this Thesis, I study composite quantum impurities with variational techniques, both inspired by machine learning as well as fully analytic. I supplement this with exploration of other applications of machine learning, in particular artificial neural networks, in many-body physics. In Chapters 3 and 4, I study quasiparticle systems with variational approach. I derive a Hamiltonian describing the angulon quasiparticle in the presence of a magnetic field. I apply analytic variational treatment to this Hamiltonian. Then, I introduce a variational approach for non-additive systems, based on artificial neural networks. I exemplify this approach on the example of the polaron quasiparticle (Fröhlich Hamiltonian). In Chapter 5, I continue using artificial neural networks, albeit in a different setting. I apply artificial neural networks to detect phases from snapshots of two types physical systems. Namely, I study Monte Carlo snapshots of multilayer classical spin models as well as molecular dynamics maps of colloidal systems. The main type of networks that I use here are convolutional neural networks, known for their applicability to image data.}, author = {Rzadkowski, Wojciech}, issn = {2663-337X}, pages = {120}, publisher = {Institute of Science and Technology Austria}, title = {{Analytic and machine learning approaches to composite quantum impurities}}, doi = {10.15479/at:ista:10759}, year = {2022}, } @phdthesis{8958, abstract = {The oft-quoted dictum by Arthur Schawlow: ``A diatomic molecule has one atom too many'' has been disavowed. Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the rotation of coupled cold molecules in the presence of a many-body environment. In this thesis, we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron - a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon - a quasiparticle formed out of a rotating molecule in a bosonic bath. With this theoretical toolbox, we reveal the self-localization transition for the angulon quasiparticle. We show that, unlike for polarons, self-localization of angulons occurs at finite impurity-bath coupling already at the mean-field level. The transition is accompanied by the spherical-symmetry breaking of the angulon ground state and a discontinuity in the first derivative of the ground-state energy. Moreover, the type of symmetry breaking is dictated by the symmetry of the microscopic impurity-bath interaction, which leads to a number of distinct self-localized states. For the system containing multiple impurities, by analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system from the strong-coupling regime to the weak molecule-bath interaction regime. We show that the molecules tend to have a strong alignment in the ground state, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. Finally, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.}, author = {Li, Xiang}, issn = {2663-337X}, pages = {125}, publisher = {Institute of Science and Technology Austria}, title = {{Rotation of coupled cold molecules in the presence of a many-body environment}}, doi = {10.15479/AT:ISTA:8958}, year = {2020}, } @phdthesis{1189, abstract = {Within the scope of this thesis, we show that a driven-dissipative system with few ultracold atoms can exhibit dissipatively bound states, even if the atom-atom interaction is purely repulsive. This bond arises due to the dipole-dipole inter- action, which is restricted to one of the lower electronic energy states, resulting in the distance-dependent coherent population trapping. The quality of this al- ready established method of dissipative binding is improved and the application is extended to higher dimensions and a larger number of atoms. Here, we simu- late two- and three-atom systems using an adapted approach to the Monte Carlo wave-function method and analyse the results. Finally, we examine the possi- bility of finding a setting allowing trimer states but prohibiting dimer states. In the context of open quantum systems, such a three-body bound states corre- sponds to the driven-dissipative analogue of a Borromean state. These states can be detected in modern experiments with dipolar and Rydberg-dressed ultracold atomic gases. }, author = {Jochum, Clemens}, pages = {94}, publisher = {Technical University Vienna}, title = {{Dissipative Few-Body Quantum Systems}}, year = {2016}, }