Speaker
Description
The eigenstate thermalization hypothesis (ETH), the leading conjecture for the emergence of statistical mechanics in quantum systems, is formulated in terms of matrix elements of observables. However, much stronger statements about chaotic systems are available from the structure of their eigenstates. The ETH has recently been reinterpreted in terms of the mathematical subject of free probability theory. I discuss this connection and argue that its extension to chaotic eigenstates yields a powerful diagrammatic framework whose connected components I refer to as generalized free cumulants. Using these diagrams, I discuss how time-dependent quantities such as reduced density matrices and entanglement entropy reach thermal equilibrium and provide insight into the Page curve for entanglement entropy.
| Academic year | 3rd year |
|---|---|
| Research Advisor | Pavan Hosur |
