Research Projects

The proposal aims to understand nonlinear dynamics in dissipative quantum systems by focusing on the quantum regime. The formalism of open quantum systems relies on the construction and solution of quantum master equations, which are challenging and nontrivial. There is no systematic method to quantize paradigmatic classical oscillators, such as van der Pol or Kuramoto oscillators, to study them in the quantum regime. 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. Recent studies have shown that the notion of synchronization exhibits counterintuitive results that cannot be understood from its classical analog. The manifestation of oscillation quenching and symmetry breaking states in the quantum regime differs from their classical counterparts due to the presence of inherent quantum noise, quantization in energy levels, and the effect of inherent quantum processes, such as entanglement and wave function collapse. The project aims to quantify classical oscillators to obtain their equivalent quantum master equation, explore network dynamics of quantum oscillators under arbitrary coupling topology, and investigate how synchronization and symmetry breaking states are connected to a paradigmatic quantum phenomenon, namely entanglement. The answer to these questions will lead to a better understanding of the connection between classical and quantum nonlinear dynamics.