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Understanding nonlinear dynamics in dissipative quantum systems has recently been a topic of
extensive research. This study requires formalisms of open quantum system that rely on the
construction and solution of quantum master equations, which are nontrivial and thus challenging.
The well known dynamical manifestations of a single unit, such as limit cycle, and emergent
dynamics of coupled oscillators, such as synchronizations and symmetry breaking behave
differently in the quantum regime. This may be attributed to the fact that quantum oscillations are
bounded by several constraints of quantum mechanics (e.g., Heisenberg uncertainty principle and
entanglement). In this talk I will systematically introduce the concept of quantum limit cycle using
the open quantum formulation and discuss some intriguing emergent dynamics of coupled quantum
oscillators. |