Optimized auxiliary oscillators for the simulation of general open quantum systems

Abstract

A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation for the system and the modes may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly non-perturbative coupling regimes and at arbitrary temperatures including zero. We apply the method to an exactly solvable problem in order to demonstrate its accuracy, and present two studies based on current research in the context of coherent transport in biological aggregates and organic photovoltaics as more realistic examples of its use and potential; performance and versatility are highlighted, and theoretical and numerical advantages over existing methods, as well as possible future improvements, are discussed.

Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes

“…Finally, a current open problem relating to construction of the master equation is how to convert between the pathological and Lindblad form for when the OQS couples to more than two discrete modes with complex coefficients; as far as we are aware, no generalized form of transformation matrix allowing for the conversion has been determined beyond this case (although see perhaps the related inversion problem explored in Appendix C of Ref. [47]). Therefore, future work in this area could focus on developing a systematic approach to regularizing the master equation for arbitrarily complicated environment structures, which in itself would likely rely on a numerical implementation.…”

Nonequilibrium dual-boson approach

“…Following Ref. 47 we stress that although the auxiliary Bose bath is taken at zero temperature this does not restrict the temperature of Bose bath in the physical system: the information about finite temperature will be provided by parameters of the auxiliary Bose modes. Finally note that parameters m1m2 , t mn , ω β1β2 , r β m1m2 , Γ (L) n1n2 , Γ (R) n1n2 and γ (P ) β1β2 of the Lindblad equation (B1)-(B2) are used to fit hybridization functions (B5) and (B14) of the physical system with corresponding hybridization functions (B3) and (B11) of the auxiliary model employing a cost function to quantify deviation 49 .…”

“…Accurate choice of the reference system parameters was recently discussed in Refs. 46,47 for Bose baths and in Refs. 48,49 for Fermi baths.…”

Universal anti-Kibble-Zurek scaling in fully-connected systems

“…In order to verify the previous AKZ scaling relations, we consider the system interacting weakly with a Markovian bath at temperature T , although similar results are found considering a more realistic scenario [78], including non-Markovian effects via the non-perturbative approach developed in [81,82]. Thus, consider for now the dynamics fixed by the master equation [46,47]…”