Exact Classicalization of N-Level Quantum Systems Interacting with a Bath: Theory and Applications

In this manuscript, starting from a five-step algorithmic procedure for exactly classicalizing the dynamics of N-level quantum systems, we incorporate a classical bath of harmonic oscillators to model environmental interactions. Using the geometry of complex projective spaces CP(N-1) and a Langevin formalism, we obtain N-1 Hamilton's equations which encode both the quantum system and the bath degrees of freedom, representing a generalization of the Caldeira-Legget model in a complex projective space. We demonstrate the efficacy of the method by applying it to two paradigmatic systems: a two-qubit system in CP(3) under entangling interactions, reproducing quantum observables such as state populations, quaternionic population differences and concurrence, and the seven-state Fenna-Matthews-Olson (FMO) complex in CP(6), reproducing state populations in the picosecond timescale.