Dabelow, Lennart: Predicting quantum many-body dynamics out of equilibrium. 2021
Inhalt
- Motivation
- Context and concepts
- Quantum and statistical mechanics
- Equilibration and thermalization
- Typicality and concentration of measure
- Perturbed relaxation
- Aims and setup
- Prerequisites
- Perturbation ensembles
- Eigenvector overlap moments
- Resolvent approach and supersymmetry methods
- Second moment and overlap distribution
- Fourth moment
- Alternative approach and higher-order moments
- Prethermalization
- Typical time evolution
- Examples
- Connections, flaws, and prospects
- Echo dynamics
- Echo protocols and irreversibility
- Classical examples
- Imperfect preparation
- Imperfect reversal
- Combined effect and discussion
- Driven systems
- Conclusions
- Acknowledgments
- Abbreviations and conventions
- Supersymmetry methods
- Anticommuting numbers and graded algebra
- Linear algebra in superspaces
- Differentiation and integration
- Gaussian integrals
- Commuting variables
- Anticommuting variables
- Supersymmetric variables
- Hubbard-Stratonovich transformation
- Saddle-point approximation
- Details on derivations
- Ensemble variance of the dynamics under diagonal perturbations (Sec. 3.2)
- Saddle-point integral for the fourth overlap moment (Sec. 3.4.3)
- Example for the alternative overlap-moment approximation (Sec. 3.4.4)
- Exploiting ensemble properties for the prethermalization bound (Sec. 3.5)
- Bound for the remnant term in the ensemble-averaged dynamics (Sec. 3.6.3)
- Ensemble variance of the echo signal under imperfect preparation (Sec. 4.3.1)
- References