IQI Weekly Seminar

Abstract: In recent years, the fundamental mechanism of thermalization of isolated many-body quantum systems has attracted renewed attentions, in light of quantum statistical mechanics, quantum information theory, and quantum technologies. In particular, it has been recognized that the eigenstate thermalization hypothesis (ETH) plays a crucial role in understanding the mechanism of thermalization, which states that even a single energy eigenstate is thermal if the system is quantum chaotic.

In this talk, I will discuss our recent results on the second law of thermodynamics for pure quantum states [1].   In our setup, the entire system obeys unitary dynamics, where the initial state of the heat bath is not the Gibbs ensemble but a single energy eigenstate.   Our proof is mathematically rigorous, and the Lieb-Robinson bound plays a crucial role.   In addition, I will talk about our numerical result on large deviation analysis of the ETH [2], which directly evaluates the number of athermal energy eigenstates and validates the ETH.    Our results would reveal a general scenario that thermodynamics emerges purely from quantum mechanics.

[1] E. Iyoda, K. Kaneko, and T. Sagawa, Phys. Rev. Lett. 119, 100601 (2017). 
[2] T. Yoshizawa, E. Iyoda, and T. Sagawa, Phys. Rev. Lett. 120, 200604 (2018).