The density operador which describes an ensemble, [tex](adsbygoogle = window.adsbygoogle || []).push({});

\rho = \sum_{i} w_i |a_i> <a_i|[/tex] (represented in the basis in which it is diagonal), evolves in time such that [tex]|a_i(t)> = U(t) |a_i> [/tex]when the enemble remains undisturbed, i.e. the w_i do not change.

But for irreversible processes the w_i may change towards a more random ensemble, driving the density matrix to a diagonal form with equal values for the w_i.

This is what I got after reading chapter 3.4 of Sakurai´s Modern Quantum Mechanics. But what Sakurai does not explain is how the time evolution of the w_i may look like for irreversible processes. May be someone can give a hint or a reference.

The background of my question: I´ve read that a transition from a pure ensemble (density matrix has only one element different from zero) to a mixed ensemble (with several w_i different from zero) is not allowed in QM (I read this in relation with black holes). I would like to understand why.

Thanks.

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# Time evolution of ensembles

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