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A. Neumaier
Mar8-12, 08:51 AM
Sci Advisor
P: 1,943
Quote Quote by Ken G View Post
Not quite-- that paper requires that the bath molecules have much larger mass than the quantum particles, whereas I get the sense the OP is interested in just more water inside of water. In other words, the paper seems to focus on situations where the "cut" is imposed by a greater "classicalness" of the individual particles in the bath, rather than by the sheer weight of numbers of the particles in the bath. It's still clearly an interesting and relevant reference though! It would seem the next step is to try to generalize that type of approach for systems of large numbers of molecules rather than high mass molecules, but it will require an approach that doesn't expand in a small parameter (or finds some other clever way to do that).
If the environment consists of different particles than the single molecule, the situation is similar, even if the molecule is as heavy or heavier than the particles in the environment.

But a water molecule surrounded by water is different as the different water molecules are indistinguishable. (A practical question is: How does one remember which molecule was singled out, as all are indistinguishable?)

In any case, the answer is here given by the 1-particle reduced density operator of statistical mechanics (if the water molecule is considered as asingle particle). See. e.g., Chapter 7F of Reichl's book on statistical Physics.