The Phase-Coupled Caldeira-Leggett Model: Non-Markovian Open Quantum Dynamics beyond Linear Dissipation

We introduce the Phase-Coupled Caldeira-Leggett (PCL) model of quantum dissipation and develop an exact framework for its dynamics. Unlike the conventional Caldeira-Leggett model with linear system-bath coupling H_SBproptohat F, the PCL model features an exponential interaction H_SBpropto e^{iλhat F}, where hat F denotes the collective bath coordinate. This model unifies concepts from quantum Brownian motion and polaron physics, providing a general platform to study phase-mediated dissipation and decoherence beyond the linear-response regime. Despite its nonlinear system-bath coupling, the Gaussian nature of the environment allows a nonperturbative and non-Markovian treatment of PCL model within the algebra of dissipative quasiparticles. We obtain an exact closed-form equation of motion for the reduced density operator, and numerical simulations reveal distinctive dynamical behaviors that deviate markedly from those predicted by the conventional Caldeira-Leggett model.