Thermalization, Chaos and Out-of-time-ordered correlators in Quantum field theory

Bhattacharya, Abhirup (2019) Thermalization, Chaos and Out-of-time-ordered correlators in Quantum field theory. Masters thesis, Indian Institute of Science Education and Research, Kolkata.

PDF (MS dissertation of Abhirup Bhattacharya (14MS140)) 14MS140.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

We will investigate the notions of thermalization and chaos in the context of quantum field theories. We will first attempt to quantify quantum information spreading through simple lattice systems and then define thermalization as the spread of entanglement across the system. We will then study the notion of operator growth and introduce our main player: the squared commutator and its cousin the OTOC. The rate of growth of the OTOC, it turns out, is identical to the rate of spread of entanglement. We will give a heuristic argument demonstrating this fact. In order the compute the OTOC for quantum field theories we will introduce a contour in the complex plane with two real time folds. After inserting external and interaction vertices at appropriate places in the contour we draw the ensuing Feynman diagrams and do a full pertubative computation of the squared commutator. We sum a special class of diagrams called ladder diagrams which furnishes a recursion relation in the form of an integral equation. The maximal eigenvalue of this equation is defined as a quantum Lyapunov exponent. We carry out this computation for two representative models: a large-N matrix ∅⁴ and QED₃ with a large number of fermionic flavours. In both the cases we compute the Lyapunov exponent as a function of the free parapmeters of the theories.

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