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A large class of isolated quantum system in a pure state can equilibrate andserve as a heat bath. We show that once the equilibrium is reached, any of itssubsystems that is much smaller than the isolated system is thermalized suchthat the subsystem is governed by the Gibbs distribution. Within thistheoretical framework, the celebrated superposition principle of quantummechanics leads to a prediction of a thermalized subsystem with multipletemperatures when the isolated system is in a superposition state of energyeigenstates of multiple distinct energy scales. This multiple-temperature stateis at equilibrium, completely different from a non-equilibrium state that hasmultiple temperatures at different parts. Feasible experimental schemes toverify this prediction are discussed.

Quantum thermalization and equilibrium state with multiple temperatures