Threshold between macroscopic behavior of matter and quantum behavior

[frankinstein]

I have question regarding the threshold between macroscopic behavior of matter and quantum behavior. Is there a range where matter acts as both or is there a sharp cut-off point from quantum behavior to macro behavior?

Frank

 

[0xDEADBEEF]

In a way your question is ill put. Everything behaves according to quantum dynamics. What really happens in the classical limit is, that we stop tracking all the information that we need for quantum predictions and start with statistics.
To give you a more satisfying answer if you want more than 10 molecules to show the typical quantum behavior that you probably have in mind, you have to put in a lot of work. On the other hand there are a lot of things that you probably wouldn't call quantum, which cannot be explained without quantum mechanics, like color.

 

[f95toli]

There a few examples where one can observe a transition from what is usually referred to "classical" behaviour to "true quantum" behaviour. A typical example would be the transition from thermal activation to quantum tunnelling in certain systems.
In these systems the transport mechanism depends on the temperature, at high temperatures one observes classical behaviour (the dynamics is e.g. governed by an Arrhenius equation) and at very low temperatures typical QM behaviour (the dynamics is governed by the Schrodinger equation, there are quantized levels etc).

Anyway, this means that there is also an intermediate temperature regime where one sees a mixture of the two and -at least in the systems I am familiar with- the mathematical expressions for the two regimes merge quite nicely.