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Motivated by recent works aimed at understanding the status of equilibrationand the eigenstate thermalization hypothesis in theories with confinement, wereturn to the 't Hooft model, the large-$N_c$ limit of (1+1)-d quantumchromodynamics. This limit has been studied extensively since its inception inthe mid-1970s, with various exact results being known, such as the quark andmeson propagators, the quark-antiquark interaction vertex, and the meson decayamplitude. We then argue this model is an ideal laboratory to studynon-equilibrium phenomena, since it is manifestly non-integrable, yet oneretains a high level of analytic control through large-$N_c$ diagrammatics. Wefirst elucidate what are the non-equilibrium manifestations of the phenomenonof large-$N_c$ volume independence. We then find that within the confinedphase, there is a class of initial states that lead to a violation of theeigenstate thermalization hypothesis, i.e. the system never thermalizes. Thisis due to the existence of heavy mesons with an extensive amount of energy, aphenomenon that has been numerically observed recently in the quantum Isingchain.

Lack of thermalization in (1+1)-d QCD at large $N_c$