Speaker: Naoto Shiraishi (Gakushuin University)

Date & Time: 2pm, Mar. 10, 2021.

Title: Undecidability in quantum thermalization phenomena

Abstract: If we leave a quantum many-body system at a nonequilibrium initial state and measure some macroscopic observable, it will relax to the unique equilibrium value. This phenomenon is called thermalization. Almost all physical systems are considered to show thermalization, while some quantum many-body systems including integrable systems do not thermalize. One of the central problems in quantum thermalization is to find the conditions to determine the presence or absence of thermalization for any given system. Despite vast literature in this field, this problem has still been left as an open problem.

We tackle this problem with a completely different approach from previous ones. We employ the viewpoint of theoretical computer science, and clarify the hardness of the problem of quantum thermalization. Surprisingly, we find that this problem is an undecidable problem [1,2]. Our result is still valid even when the system is one-dimensional, Hamiltonian is shift-invariant and nearest-neighbor interaction, the initial state is a product state, and the observable is the shift-sum of a one-body observable.

In this seminar, we first present pedagogical reviews of quantum thermalization and theoretical computer science. We then explain our main result and the outline of its proof.

References:
[1] N. Shiraishi and K. Matsumoto, arXiv:2012.13889
[2] N. Shiraishi and K. Matsumoto, arXiv:2012.13890