Analytic and machine learning approaches to composite quantum impurities
Rzadkowski, Wojciech
Analytic and machine learning approaches to composite quantum impurities - Institute of Science and Technology Austria 2022
Thesis
Abstract Acknowledgments About the Author List of Publications Table of Contents List of Figures 1 Introduction 2 Methods 3 Variational approach to spinful angulon 4 Neural-network quantum states approach to the polaron Hamiltonian 5 Characterizing phase transitions with convolutional neural networks 6 Conclusions Bibliography
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.
Analytic and machine learning approaches to composite quantum impurities - Institute of Science and Technology Austria 2022
Thesis
Abstract Acknowledgments About the Author List of Publications Table of Contents List of Figures 1 Introduction 2 Methods 3 Variational approach to spinful angulon 4 Neural-network quantum states approach to the polaron Hamiltonian 5 Characterizing phase transitions with convolutional neural networks 6 Conclusions Bibliography
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.