Application of stochastic Liouville–von Neumann equation to electronic energy transfer in FMO complex

Exactly thermalized quantum dynamics of the spin-boson model coupled to a dissipative environment

“…In our previous work [15], a method for noise generation was proposed which we shall review and further develop here, introducing a modified noise generation scheme that diminishes the exponential growth of the trace of the density matrix which seems to characterize these methods. This is the latest in a series of proposals aimed at tackling this problem [16,17].…”

“…It is typically the initial starting model for any approach that deals with open quantum systems, due to its relative simplicity while still exhibiting dissipative behavior. The model consists of a twolevel spin system surrounded by bosonic degrees of freedom that describe the environment, and can naturally be applied to qubits coupled to an environment [18][19][20][21][22], electronic energy transfer in biological systems [16], Josephson junctions [23][24][25], cold atoms [26,27], and solid-state artificial atoms [28]. The spin-boson model has already been considered previously by us in the context of the ESLN [15]; however, due to a recently discovered implementation error, the numerical results were inaccurate.…”

A variance reduction technique for the stochastic Liouville–von Neumann equation

“…With the notable exception of Ref. [23], this optimization was not attempted in previous work, and the non-physical correlations were chosen with an eye to easy numerical noise generation [14,24,25]. ξ was decomposed into a sum of independent terms ξ l ∈ R and ξ s ∈ C with…”

Time-correlated blip dynamics of open quantum systems

“…They apply to systems with discrete Hilbert space as well as continuous degrees of freedom and have the particular benefit that they allow for a natural inclusion of external time dependent fields irrespective of amplitude and frequency. Specific applications comprise spin-boson dynamics [35], optimal control of open systems [37], semiclassical dynamics [47], molecular energy transfer [36], generation of entanglement [48], and heat and work fluctuations [49,50], to name but a few.…”

“…In fact, influence functionals do not only arise when a partial trace is taken over environmental degrees of freedom, they are also representations of random forces sampled from a classical probability space [25]. This stochastic construction can be reversed, leading to an unraveling of quantum mechanical influence functionals into time-local stochastic action terms [33]; we thus obtain the dynamics of the reduced system through statistical averaging of random state samples generated by numerically solving a single time-local stochastic Liouvillevon Neumann equation (SLN [35][36][37]). Compared to other methods this provides a very transparent formulation of nonMakrovian quantum dynamics with the particular benefit that the consistent inclusion of external time dependent fields is straightforward [37].…”