Dissipative evolution of a two-level system through a geometry-based classical mapping

Abstract In this manuscript, we introduce a geometry-based formalism to obtain a Meyer–Miller–Stock–Thoss mapping in order to study the dynamics of both isolated and interacting two-level systems (TLS). After showing the description of the isolated case using classical-like canonically conjugate variables, we implement an interaction model by bilinearly coupling the corresponding population differences à la Caldeira–Leggett, obtaining a Gross–Pitaevskii-like equation. This allows us to analytically find a transition between oscillatory and tunneling block dynamics by varying the coupling constant. Extending our model to the system plus environment case, where the environment is considered as a collection of TLSs, we reveal that the dynamics become chaotic, exhibiting tunneling-suppressed dynamics in the strong coupling limit and the usual damping effect similar to that of a harmonic oscillator bath in the weak coupling one. Finally, we observe that our interacting model turns an isolated symmetric TLS into an environment-assisted asymmetric one.