Statistical mechanics and quantum entanglement

Hi everyone!

Jonathon Riddell here. Today we take a closer look at how entanglement entropy plays a role in the emergence of statistical mechanics. We find that the entanglement entropy between a part of a system obeying eigenstate thermalization, and the rest of the system, scales like the size of the subsystem. This is called a "volume law" and is a key indicator that an energy eigenstate may obey the Eigenstate Thermalization Hypothesis.

First video on ETH: https://youtu.be/p4fpzYD_WRU

Density matrices: https://youtu.be/1tserF6VGqI

To view my publication history: https://scholar.google.com/citations?user=V2UZXZMAAAAJ&hl=en

00:00 Intro and announcements 02:30 Constructing our Hilbert space 08:24 Density matrix essentials 13:17 Reviewing ETH prediction 15:30 Entanglement for pure states 18:23 Von Neumann entropy and scaling 21:51 Entanglement entropy volume law ... https://www.youtube.com/watch?v=Y6OQagIXAHU