Background
The question here by Prof. Wen, and the answers that follow point out that spontaneous symmetry breaking (SSB) has something to do with decoherence if I understand it crudely correctly.
But the usual reasoning why SSB does not occur in a quantum mechanical system (for example, a particle confined in a double-well potential) is that (due to the tunnelling effects) the ground state is a symmetric or antisymmetric linear superposition of the ground state wavefunctions localized around the classical minima of the potential which respects the symmetry of the Hamiltonian. It's only in field theory where one has infinite degrees of freedom and the tunnelling effects are shut down so that one can have SSB.
Question
If decoherence were truly the reason of SSB then should one not expect SSB to happen even in quantum mechanics, and the system to go to a mixed state? But SSB doesn't happen in quantum mechanics.
I guess I wrongly understood the points explained there, and I would like to be clarified on this issue.
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