Full macroscopic thermalization and the formation of Schr\"odinger's cats by unitary time evolution in the weakly perturbed Ising model - Applications of the Roos-Sugimoto-Teufel-Tumulka-Vogel theory

Abstract

We study macroscopic thermalization in the ferromagnetic Ising model with a weak generic (highly nonlocal and many-body) random quantum perturbation. We prove that a single typical perturbation makes every initial state $|\Phi(0)\rangle$ in a specified energy shell thermalize: a measurement of a large class of macroscopic observables in the time-evolved state $|\Phi(t)\rangle=e^{-i\widetilde H_Lt}|\Phi(0)\rangle$ yields their thermal equilibrium values, within a prescribed precision and with overwhelming probability, at sufficiently large, typical times $t$. The result covers the full finite-temperature range, including the ordered phase, where we use plus boundary conditions. With periodic boundary conditions in the ordered phase, every energy eigenstate in the shell is shown to be an almost balanced macroscopic Schr\"odinger-cat state. Moreover, every pure initial state becomes such a cat at sufficiently large, typical times, with each branch in the corresponding macroscopic thermal equilibrium. The proof combines the theory of Roos, Sugimoto, Teufel, Tumulka, and Vogel with rigorous Ising large-deviation estimates.