Pseudomode elimination works for nonlinearly intercoupled modes in cQED whenever the eliminated sector's self-energy on the retained subsystem is rational, enabling finite damped auxiliaries independent of retained nonlinearities.
Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of mo- tion (HEOM), Journal of Chemical Physics153, 020901 (2020)
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An extensive theory of nonlinearly intercoupled pseudomodes for noise model reduction in circuit QED
Pseudomode elimination works for nonlinearly intercoupled modes in cQED whenever the eliminated sector's self-energy on the retained subsystem is rational, enabling finite damped auxiliaries independent of retained nonlinearities.