Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation

• URL: http://arxiv.org/abs/2103.01808v5
• Date: Tue, 11 Jan 2022 06:38:15 GMT
• Title: Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
• Authors: Berislav Buca, Cameron Booker, Dieter Jaksch
• Abstract summary: Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. We develop a general theory based on novel necessary and sufficient criteria for persistently oscillating eigenmodes. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.

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