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If a quantum system interacts with a "big" quantum system, you have dephasing.

The models of decoherence all have this atog aproach to them, about what is to understood of the interaction of the quantum state with a bath.

At which point does the bath character of the "bigger" system strike? In which way are the systems involved in decoherence fundamentally different? Why is it clear that a bath will behave in such and such way, that the phases vanish?

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From a theoretical point of view, a bath must be of infinite extent (infinitely many essentially independent degrees of freedom, typically involving a thermodynamic limit) in order that it can serve as a decohering environment, as otherwise unitarity implies reversibility, and no decoherence can take place.

From a practical point of view, this means that the bath must be large enough that recurrence times are several order of magnitudes higher than the time scale of interest.

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