Many Faces of Many-Body Quantum Chaos: From Periodic Orbits to Semiclassical Fields and Back
Abstract/Contents
- Abstract
- The conventional paradigm for statistical physics starts with the assumption that all microstates of an isolated system are equally probable in equilibrium. In classical mechanics, due to inherent non-linearities in the equations of motion, an ensemble of states concentrated in a small region of phase space very rapidly explore the entire allowable phase space. This ergodic property justifies the fundamental statistical assumption. In quantum mechanics, however, Schrodinger evolution is always linear in Hilbert space and ergodicity in the naïve sense does not apply. In this thesis, we explore one notion of quantum ergodicity: random matrix statistics of the energy spectrum. For few-body quantum systems that admit a semiclassical limit, Andreev et al. (arXiv:cond-mat/9601001) have proven that this notion of quantum ergodicity follows directly from the classical notion of ergodicity. We extend this work in two ways, first to many-body quantum systems (including various large N systems familiar in high energy physics) with emergent semiclassical limits, and then to a class of many-body Floquet spin chains with no semiclassical limit. In the end, we discuss limitations of our approach and make some comments on future directions to pursue.
Description
| Type of resource | text |
|---|---|
| Date created | July 7, 2020 |
Creators/Contributors
| Author | Shi, Zhengyan Darius |
|---|---|
| Primary advisor | Hartnoll, Sean |
| Primary advisor | Shenker, Stephen |
| Degree granting institution | Stanford University, Department of Physics |
Subjects
| Subject | Quantum Chaos |
|---|---|
| Subject | BGS conjecture |
| Subject | Large N systems |
| Subject | Floquet systems |
| Subject | Quantum Dynamics |
| Genre | Thesis |
Bibliographic information
| Related item | |
|---|---|
| Location | https://purl.stanford.edu/nm562zj4764 |
Access conditions
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Preferred citation
- Preferred Citation
- Shi, Zhengyan Darius. (2020). Many Faces of Many-Body Quantum Chaos: From Periodic Orbits to Semiclassical Fields and Back. Stanford Digital Repository. Available at: https://purl.stanford.edu/nm562zj4764
Collection
Undergraduate Theses, Department of Physics
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- Contact
- zdshi@mit.edu
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