Abnormalities of Chaotic Systems found in the Entanglement States of Quantum Scars
By Victoria
Ergodicity, the ability of a system to explore all accessible phase states, is a fundamental assumption in statistical mechanics, particularly in the thermodynamic representations of many-body systems. However, not all many-body systems are ergodic. Quantum scars represent a weaker form of ergodicity breaking, where certain eigenstates exhibit atypically low entanglement and resist full thermalization, leading to long-lived coherent dynamics. Partnering with VTech professor Dr. Tianci Zhou, this project looks to numerically investigate the entanglement of eigenstates of Hamiltonians, which will be used to reproduce the low-entanglement signatures found in the quantum scars phenomenon. By analyzing how these anomalous entanglement patterns evolve in time or scale with system size, we aim to ultimately gain insight into the behavior of quantum scars and their underlying mechanisms in many-body localization, constrained dynamics, and related non-equilibrium phenomena.
Files and Resources
"Average Entropy of a Subsystem" Paper
A 1993 paper by Don N. Page deriving an approximation for calculating the average entropy (information) for a quantum system of Hilbert space dimension mn. This project would aim to confirm and compare entropy calculations of many-body systems with the approximation derived in this paper.
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