Sünderhauf, Christoph (2021): Chaos in manybody quantum systems. Dissertation, LMU München: Faculty of Physics 

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Suenderhauf_Christoph.pdf 3MB 
Abstract
Chaos in manybody quantum systems is of great importance to both manybody physics as well as black hole physics. In the field of manybody physics, interactions and disorder in the system can lead to various dynamic phenomena, be it thermalisation, manybody localisation, chaotic behavior and scrambling of quantum information. In the field of high energy physics, the holographic principle connects chaos and scrambling in manybody quantum systems with the informationtheoretic properties of black holes. Theoretical quantum physics provides the framework for the models, methods, and results in this thesis, while black hole physics partly provides some motivation and inspiration. First, we introduce a new model for a manybody quantum system based on random quantum circuits. These are a popular framework for theoretic study of disordered spin chains. By drawing the random unitaries in the circuit from different ensembles, we can adjust the disorder strength in the interactions, which in turn leads to a thermal/manybody localisation phase transition. Next, we study the Brownian SYK model, a disordered model of Majorana fermions with alltoall interactions, motivated by its link to the holographic principle. We develop a new numerical method based on an effective permutational symmetry to reduce computational cost from exponential to linear or quadratic in system size N. As a consequence, we can compute scrambling quantifiers in detail, and find a log N scrambling time, as conjectured in the context of fast scrambling for black holes. Finally, we develop a model based on the continuoustime limit of a random quantum circuit. It serves as a microscopic toy model for the evaporation of a black hole. With a similar method as developed for the Brownian SYK model, we can analyse its information theoretic properties. In particular, we follow established protocols for information retrieval from the Hawking radiation. We find a separation of time scales for entanglement growth and information retrieval, related to the intrinsic black hole dynamics (∝log N) and the coupling to the environment (∝N).
Item Type:  Theses (Dissertation, LMU Munich) 

Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  21. April 2021 
1. Referee:  Schilling, Christian 
MD5 Checksum of the PDFfile:  4c9380f887e4bb73225e1466e07dc1e6 
Signature of the printed copy:  0001/UMC 27896 
ID Code:  27862 
Deposited On:  05. May 2021 13:32 
Last Modified:  05. May 2021 13:33 