Abstract
Time-independent systems possess a continuous time translation symmetry which says that eigenstates of the Hamiltonian are also eigenstates of the time translation operator. In the present chapter we analyze if this symmetry can be spontaneously broken into a discrete time translation symmetry in a quantum many-body system that would correspond to spontaneous emergence of a periodic motion of a system and thus formation of a time crystal. We also present the idea of classical time crystals.
Published Version
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