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- Is the evolution of an isolated system always periodic in QM?

If we prepare a macroscopic system (something like Shrodinger's cat) in a known quantum-mechanical state and we let it evolve for a very long time completely isolated, for what I understand the position of all it's particles will become more and more spread in space.

But if the evolution of the system is unitary, shouldn't it end up returning to the initial state after a very long time?

If not, then how will the indeterminacy of the system's state will evolve? Will it reach a state that is a superposition of all possible states with even probabilities?

But if the evolution of the system is unitary, shouldn't it end up returning to the initial state after a very long time?

If not, then how will the indeterminacy of the system's state will evolve? Will it reach a state that is a superposition of all possible states with even probabilities?