Non-stationary quantum many-body dynamics
Abstract: The assumption that quantum systems relax to a stationary (time-independent) state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. We will discuss simple algebraic conditions that lead to a quantum many-body system never reaching a stationary state, not even a non-equilibrium one. This unusual state of matter characterized by persistent oscillations has been recently called a time crystal. We show that its existence can be either related to the symmetry properties of the an isolated system, or can be, counter-intuitively, induced through the dissipation itself.
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