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Table of Contents
Supervisor's Foreword; Acknowledgments; Supplementary Material; Contents; Acronyms; 1 Introduction; 1.1 Bose
Einstein Condensation; 1.2 The Many-Body Physics of Tunneling; 1.3 Theoretical Description of Quantum Many-Body Systems; 1.4 Structure of this Thesis; References; 2 Theoretical Concepts and Numerical Methods; 2.1 The Schrödinger Equation from a Many-Body Perspective; 2.1.1 Second Quantization; 2.1.2 Quantities of Interest; 2.2 Theoretical Methods Employing the Full Many-Boson Hamiltonian; 2.2.1 The Time-Dependent Variational Principle
2.2.2 The Time-Dependent Gross
Pitaevskii Equation2.2.3 Best Mean-Field; 2.2.4 The Multiconfigurational Time-Dependent Hartree Method for Bosons; 2.3 Theoretical Methods Employing Model Hamiltonians; 2.3.1 Bose
Hubbard and Time-Evolved Block Decimation; 2.3.2 The Discrete Non-Linear Schrödinger Equation; 2.4 Numerical Methods; 2.4.1 The Multiconfigurational Time-Dependent Hartree for Bosons Software Package; References; 3 Benchmarks with Analytically Solvable Problems; 3.1 The Harmonic Interaction Model; 3.2 Benchmark Studies with the Harmonic Interaction Model; 3.2.1 One-Dimensional HIM
3.2.2 Two-Dimensional HIM3.3 Dynamics of an Interaction Quench in the Harmonic Interaction Model; 3.4 Comment on the Effects of the Separability of the Harmonic Interaction Model; 3.5 Discussion and Summary of the Benchmark with the Harmonic Interaction Model; References; 4 A Case Study with an Attractive BEC: Comparison of Lattice Model, Gross
Pitaevskii, and MCTDHB Predictions on a Tunneling Process; 4.1 Mapping of Discrete and Continuous Space Problems; 4.2 Comparison of DNLS, BH, TDGP and MCTDHB Dynamics; References
5 Theoretical Considerations and Analytical Models on the Many-Body Physics of Tunneling Bosons5.1 Analytical Considerations within the Gross
Pitaevskii Approximation; 5.2 Analytical Considerations Beyond Gross
Pitaevskii; 5.2.1 Decomposition of Hilbert Space into Subspaces; 5.2.2 Model for the Energetics of the Many-Body Physics of Tunneling to Open Space; 5.2.3 Model with Two Momenta from Single-Particle States; References; 6 Tunneling of a Many-Boson System to Open Space Without a Threshold; 6.1 One-Body Density and Integrals on It; 6.2 Momentum Distributions
6.3 Coherence from Natural Occupations and Correlation Functions6.4 Tunneling without a Threshold and Stronger Interactions; 6.5 Direct Detection of the Momentum Spectra; 6.6 Comparison of Numerics and Models; References; 7 Tunneling of a Many-Boson System to Open Space with a Threshold; 7.1 Setup; 7.2 Threshold Potentials and Their Dynamics from the Point of View of Energetics; 7.3 Controlling the Dynamics of Two Bosons by the Threshold; 7.4 Controlling the Dynamics of Three Bosons by the Interactions; 7.4.1 Nonescape Probabilities
Einstein Condensation; 1.2 The Many-Body Physics of Tunneling; 1.3 Theoretical Description of Quantum Many-Body Systems; 1.4 Structure of this Thesis; References; 2 Theoretical Concepts and Numerical Methods; 2.1 The Schrödinger Equation from a Many-Body Perspective; 2.1.1 Second Quantization; 2.1.2 Quantities of Interest; 2.2 Theoretical Methods Employing the Full Many-Boson Hamiltonian; 2.2.1 The Time-Dependent Variational Principle
2.2.2 The Time-Dependent Gross
Pitaevskii Equation2.2.3 Best Mean-Field; 2.2.4 The Multiconfigurational Time-Dependent Hartree Method for Bosons; 2.3 Theoretical Methods Employing Model Hamiltonians; 2.3.1 Bose
Hubbard and Time-Evolved Block Decimation; 2.3.2 The Discrete Non-Linear Schrödinger Equation; 2.4 Numerical Methods; 2.4.1 The Multiconfigurational Time-Dependent Hartree for Bosons Software Package; References; 3 Benchmarks with Analytically Solvable Problems; 3.1 The Harmonic Interaction Model; 3.2 Benchmark Studies with the Harmonic Interaction Model; 3.2.1 One-Dimensional HIM
3.2.2 Two-Dimensional HIM3.3 Dynamics of an Interaction Quench in the Harmonic Interaction Model; 3.4 Comment on the Effects of the Separability of the Harmonic Interaction Model; 3.5 Discussion and Summary of the Benchmark with the Harmonic Interaction Model; References; 4 A Case Study with an Attractive BEC: Comparison of Lattice Model, Gross
Pitaevskii, and MCTDHB Predictions on a Tunneling Process; 4.1 Mapping of Discrete and Continuous Space Problems; 4.2 Comparison of DNLS, BH, TDGP and MCTDHB Dynamics; References
5 Theoretical Considerations and Analytical Models on the Many-Body Physics of Tunneling Bosons5.1 Analytical Considerations within the Gross
Pitaevskii Approximation; 5.2 Analytical Considerations Beyond Gross
Pitaevskii; 5.2.1 Decomposition of Hilbert Space into Subspaces; 5.2.2 Model for the Energetics of the Many-Body Physics of Tunneling to Open Space; 5.2.3 Model with Two Momenta from Single-Particle States; References; 6 Tunneling of a Many-Boson System to Open Space Without a Threshold; 6.1 One-Body Density and Integrals on It; 6.2 Momentum Distributions
6.3 Coherence from Natural Occupations and Correlation Functions6.4 Tunneling without a Threshold and Stronger Interactions; 6.5 Direct Detection of the Momentum Spectra; 6.6 Comparison of Numerics and Models; References; 7 Tunneling of a Many-Boson System to Open Space with a Threshold; 7.1 Setup; 7.2 Threshold Potentials and Their Dynamics from the Point of View of Energetics; 7.3 Controlling the Dynamics of Two Bosons by the Threshold; 7.4 Controlling the Dynamics of Three Bosons by the Interactions; 7.4.1 Nonescape Probabilities