Electronic state mixing along branching paths

1 Electronic state mixing along branching paths 

each electronic component (r R) should be carried by its 

As discussed above, the nuclear paths can branch due to the presence of nonadiabatic interactions. Since the electronic wavepackets are to be carried over along those branching paths, the electronic packets should also branch accordingly. Such branchings can be viewed as follows. 

It is obvious that the path is not branched by the nonadiabatic interaction, and therefore the important feature of quantum entanglement caused by nonadiabatic transition is not captured correctly in this formalism. Furthermore, in a more rigorous mathematical context, the above naive treatment of electron wavepackets along with classical paths is foimd to be not quite correct. Both of Eqs. (4.41) and (4.43) need corrections, which should be referred in [493]. 

To appropriately describe the entanglement situation induced by electronic nonadiabatic transition, we should impose the following condition 

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We here consider the following two propagation of the state (1) Continue the Ehrenfest d3mamics for the next short time interval At (denoted as path 0), and (2) let the path branch into two pieces (path 1 and 2). For the path-branching, along with the associated electronic state mixing, we prepare two vectors as the initial electronic states (at this time t)... 

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