Citing https://arxiv.org/abs/cond-mat/9403051: “Furthermore if a quantum system does possess this property (whatever it may be), then we might hope that the inherent uncertainties in quantum mechanics lead to a thermal distribution for the momentum of a single atom, even if we always start with exactly the same initial state, and make the measurement at exactly the same time.”
Then the author proceed to demonstrate that it is indeed the case. I guess it partially answers the question: quantum state thermalises and you’ll get classical thermal distribution of measurement results of at least some measurements even when measuring the system in the same quantum state.
The less initial uncertainty in energy the faster the system thermalises. That is to slow quantum thermalisation down you need to initialize the system with atoms in highly localized positions, but then you can’t know their exact velocities and can’t predict classical evolution.
Citing https://arxiv.org/abs/cond-mat/9403051: “Furthermore if a quantum system does possess this property (whatever it may be), then we might hope that the inherent uncertainties in quantum mechanics lead to a thermal distribution for the momentum of a single atom, even if we always start with exactly the same initial state, and make the measurement at exactly the same time.”
Then the author proceed to demonstrate that it is indeed the case. I guess it partially answers the question: quantum state thermalises and you’ll get classical thermal distribution of measurement results of at least some measurements even when measuring the system in the same quantum state.
The less initial uncertainty in energy the faster the system thermalises. That is to slow quantum thermalisation down you need to initialize the system with atoms in highly localized positions, but then you can’t know their exact velocities and can’t predict classical evolution.