Phonons are the quanta of vibrations in a crystal lattice. As the name suggest, phonons are already a quantum phenomena but when studying heat transfer the phonons are mostly very classical (wave mechanics, semiclassical treatment).
Usually the quantum characteristics enter into the statistics (bosons statistics) but not much else. Do phonons display any evidently quantum phenomenona?
Can there be entangled phonons? When could quantum effects for phonons become important in transport?