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. However, real-world phenomena, from life to weather patterns are persistently non-stationary. I will discuss simple algebraic conditions that prevent a quantum many-body system from ever reaching a stationary state, not even a non-equilibrium one. I call these algebraic conditions dynamical symmetries. We show that its existence can be even, counter-intuitively, induced through the dissipation itself. Using these general results I provide a general theory of quantum sychronization giving both the necessary and sufficient conditions for it to occur. I give several physically relevant examples in both closed and open quantum many-body systems, including an isolated XXZ spin chain that for which the frequency of the persistent oscillations is fractal function of the interaction strength, a quasi-1D magnet with attractor-like dynamics, and a spin-dephased Fermi-Hubbard model.
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QuCoLiMaTalks are the weekly seminar of the collaborative research center TRR 306 QuCoLiMa (Quantum Cooperativity of Light and Matter). The talks are given by (external) experts, whose research falls within the scope of QuCoLiMa.