Noise Decomposition in Stochastic Liouville Equation
题目：Noise Decomposition in Stochastic Liouville Equation
The stochastic Liouville equation (SLE) is a fruitful framework to simulate the challenging non-Markovian quantum dissipative dynamics. The working horse of SLE is an ordinary stochastic differential equation straightforward to implement in numerics. Its performance for strong dissipation, however, degrades due to the drastic increase of the numerical error at large times. Notwithstanding, SLE may serve as a starting point to derive new efficient algorithms.
We have recently revealed that noise decomposition is powerful for methodological development and will present in this talk the corresponding progress. First, via noise decomposition we have proven the equivalence between SLE and the non-Markovian quantum state diffusion. The procedure we use provides a means of calculating the unknown functional derivative in the latter and allows a feasible derivation of the rigorous master equations for the spontaneously decaying multistate systems.
Second, we have shown the unification between the formula of differentiation and the hierarchy approach. In this two methods, the stochastic differential equation is transformed into different sets of coupled, linear ordinary differential equations. By decomposing the involved noise, we have proposed a unified algorithm that may reduce to the hierarchy approach or the formula of differentiation in different limits and suggested a new class of hierarchy-like methods.
Third, we have put forward a piecewise ensemble average SLE. Starting from a conventional SLE, we can always decompose the involved noises into two parts: the principal part assuming piecewise correlations and the auxiliary part recovering the full correlation. A partial stochastic average over the auxiliary noises yields a SLE that only involves noises with piecewise correlations. The noise disentanglement in different intervals enables a piecewise ensemble average. This strategy avoids the long-time stochastic average, can greatly suppress the statistical errors at long times and is thus suitable for simulating long-time dynamics in the non-perturbative regime.