Imagine walking deep into a dense forest without a map or GPS. Initially, you kind of know where you started. But as you wander further, eventually, it's impossible to tell where you came from — every direction looks the same. That's thermalization.
The initial state's details get scrambled across all degrees of freedom and as a result local observables settle into a stable, time-independent state called the equilibrium state. The fact that macroscopic objects equilibrate with their environments is such a ubiquitous experience that understanding it doesn't seem very interesting. Although it's absolutely non-trivial. At Equilibrium these local observables are represented by their thermal expectation values.
So if one had access to a map or perhaps a GPS which just means keeping track of those initial details such as any non-local correlations or even the entire state, locally thermalization would still occur, but one could easily backtrack to the initial state. In physics it is quite surprising how systems behave collectively, when compared to the behavior of its components. This is known as emergent behavior.
We've been taught that evolution of any system should entirely depend on initial conditions but we see that a lack of initial state dependence is what actually gives a consistent behavior macroscopically.
For an isolated quantum many-body system, this becomes even more fascinating because even though the full evolution, is unitary and reversible--which means backtracking is guaranteed-- locally, memory seems to be lost.
Then how does this classical behaviour emerge from Quantum mechanics?
A key idea is the Eigenstate Thermalization Hypothesis (ETH): each non-degenerate energy eigenstate itself can be considered “thermal”.
Their expectation values fluctuate little between nearby eigenstates, provided the local operator acts on few degrees of freedom.
Intuitively, a small subsystem of an isolated quantum system acts as if it's in contact with a thermal bath—the rest of the system. So in large, non-integrable systems, thermal behavior emerges without needing a microcanonical average—a single eigenstate often suffices.
If ETH is true then if the initial state dependent coefficients are concentrated around some single energy then our TEV will give the desired microcanonical and canonical averages.
Our guest today is Pavan Hosur, a theoretical physicist in the Department of Physics and the Texas Center for Superconductivity at the University of Houston. His research focuses on understanding topological phases of matter, exotic broken symmetry phases, and how to detect them experimentally. He also explores quantum ergodicity, quantum chaos, and more broadly, how concepts from classical statistical mechanics extend into the quantum realm. We’re recording this episode in his lovely office, discussing how our complex yet elegant macroscopic world emerges from the quantum laws that govern the microscopic one. So let’s get started.
His website is here: https://sites.google.com/nsm.uh.edu/qmb/home
