The polaron at strong coupling
Feliciangeli, Dario
The polaron at strong coupling - Institute of Science and Technology Austria 2021
Thesis
Abstract Acknowledgements About the Author List of Collaborators and Publications Table of Contents 1 Introduction 2 Pekar Functional on a Ball 3 The Strongly Coupled Polaron on the Torus 4 Persistence of the Spectral Gap for the Landau-Pekar Equations 5 Effective Mass of the Polaron via Landau-Pekar Equations Bibliography A Non-Commutative Entropic OT and Quantum Composite Systems
This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author.
The polaron at strong coupling - Institute of Science and Technology Austria 2021
Thesis
Abstract Acknowledgements About the Author List of Collaborators and Publications Table of Contents 1 Introduction 2 Pekar Functional on a Ball 3 The Strongly Coupled Polaron on the Torus 4 Persistence of the Spectral Gap for the Landau-Pekar Equations 5 Effective Mass of the Polaron via Landau-Pekar Equations Bibliography A Non-Commutative Entropic OT and Quantum Composite Systems
This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author.