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Numerical Integration of the Kadanoff-Baym Equations
Numerical Integration of the Kadanoff-Baym Equations
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211153009
- ISBN
- 9798384044543
- DDC
- 530
- 저자명
- Blommel, Thomas.
- 서명/저자
- Numerical Integration of the Kadanoff-Baym Equations
- 발행사항
- [Sl] : University of Michigan, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 157 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
- 주기사항
- Advisor: Gull, Emanuel.
- 학위논문주기
- Thesis (Ph.D.)--University of Michigan, 2024.
- 초록/해제
- 요약In this thesis we present methodologies that have been developed to efficiently solve for the non-equilibrium Green's Function (NEGF) of interacting electron systems, and demonstrate their applications to several different condensed matter systems. These solvers are based on the numerical integration of the equations of motion for the NEGF, which are known as the Kadanoff-Baym Equations (KBE). The KBE are a general set of equations which allow for the study of a wide range of systems that are of interest to condensed matter physicists, including superconductivity, nuclear matter, molecules and atoms, and qubits, among many others. They are also useful for solving impurity models and systems in the dynamical mean-field theory (DMFT) approximation through their ability to incorporate dynamical hybridization functions.The generality of these equations comes from their connection to time-dependent Many-Body Perturbation Theory (MBPT), which introduces non-Markovian dynamical correlations through the self-energy functional. MBPT ensures important conservation laws, such as those for density and energy, are obeyed no matter the type of time-dependent perturbations that are applied to the Hamiltonian. The non-Markovian correlations manifest in a kernel that couples the dynamics to the entire history of the system. This coupling leads to computational costs that become prohibitively expensive as longer-time dynamics are probed, this is especially true for systems which decohere slowly, leading to undamped dynamics and kernels. Due to the large amount of interest in non-equilibrium quantum dynamics, the availability of efficient solvers for the KBE are of great importance. This thesis will focus on the implementation and analysis of integration methods for the KBE, including compression algorithms which lower computational complexity and adaptive integration techniques which allow for resolution of dynamics which vary over wide ranges of timescales.Chapter 1 gives an introduction to quantum systems and the problems we will be studying. Chapter 2 provides a derivation of the NEGF and its representation on the Keldysh contour. Chapter 3 derives the KBE from MBPT and introduces the self-energy and its conservation laws. Chapter 4 introduces the numerical techniques used to integrate the KBE, as well as an analysis of its causality structure. In Chapter 5, we use compression techniques to lower the complexity of the KBE, and provide details on its implementation. In Chapter 6 we apply the compression algorithm to study the Higgs mode in a superconducting system. In Chapter 7, we couple our solver to an adaptive integrator and analyze its performance against fixed-timestep integrators. Finally, Chapter 8 provides a summary of the results and an outlook for future work on efficient solvers.
- 일반주제명
- Condensed matter physics
- 일반주제명
- Physics
- 일반주제명
- Quantum physics
- 키워드
- Quantum dynamics
- 기타저자
- University of Michigan Physics
- 기본자료저록
- Dissertations Abstracts International. 86-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211153009
■006m o d
■007cr#unu||||||||
■020 ▼a9798384044543
■035 ▼a(MiAaPQ)AAI31631434
■035 ▼a(MiAaPQ)umichrackham005834
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aBlommel, Thomas.
■24510▼aNumerical Integration of the Kadanoff-Baym Equations
■260 ▼a[Sl]▼bUniversity of Michigan▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a157 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-03, Section: B.
■500 ▼aAdvisor: Gull, Emanuel.
■5021 ▼aThesis (Ph.D.)--University of Michigan, 2024.
■520 ▼aIn this thesis we present methodologies that have been developed to efficiently solve for the non-equilibrium Green's Function (NEGF) of interacting electron systems, and demonstrate their applications to several different condensed matter systems. These solvers are based on the numerical integration of the equations of motion for the NEGF, which are known as the Kadanoff-Baym Equations (KBE). The KBE are a general set of equations which allow for the study of a wide range of systems that are of interest to condensed matter physicists, including superconductivity, nuclear matter, molecules and atoms, and qubits, among many others. They are also useful for solving impurity models and systems in the dynamical mean-field theory (DMFT) approximation through their ability to incorporate dynamical hybridization functions.The generality of these equations comes from their connection to time-dependent Many-Body Perturbation Theory (MBPT), which introduces non-Markovian dynamical correlations through the self-energy functional. MBPT ensures important conservation laws, such as those for density and energy, are obeyed no matter the type of time-dependent perturbations that are applied to the Hamiltonian. The non-Markovian correlations manifest in a kernel that couples the dynamics to the entire history of the system. This coupling leads to computational costs that become prohibitively expensive as longer-time dynamics are probed, this is especially true for systems which decohere slowly, leading to undamped dynamics and kernels. Due to the large amount of interest in non-equilibrium quantum dynamics, the availability of efficient solvers for the KBE are of great importance. This thesis will focus on the implementation and analysis of integration methods for the KBE, including compression algorithms which lower computational complexity and adaptive integration techniques which allow for resolution of dynamics which vary over wide ranges of timescales.Chapter 1 gives an introduction to quantum systems and the problems we will be studying. Chapter 2 provides a derivation of the NEGF and its representation on the Keldysh contour. Chapter 3 derives the KBE from MBPT and introduces the self-energy and its conservation laws. Chapter 4 introduces the numerical techniques used to integrate the KBE, as well as an analysis of its causality structure. In Chapter 5, we use compression techniques to lower the complexity of the KBE, and provide details on its implementation. In Chapter 6 we apply the compression algorithm to study the Higgs mode in a superconducting system. In Chapter 7, we couple our solver to an adaptive integrator and analyze its performance against fixed-timestep integrators. Finally, Chapter 8 provides a summary of the results and an outlook for future work on efficient solvers.
■590 ▼aSchool code: 0127.
■650 4▼aCondensed matter physics
■650 4▼aPhysics
■650 4▼aQuantum physics
■653 ▼aNonequilibrium quantum dynamics
■653 ▼aKadanoff-Baym Equations
■653 ▼aMany-Body Perturbation Theory
■653 ▼aCompression algorithm
■653 ▼aQuantum dynamics
■690 ▼a0605
■690 ▼a0611
■690 ▼a0599
■71020▼aUniversity of Michigan▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g86-03B.
■790 ▼a0127
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17164494▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
