TY - JOUR

T1 - Efficient choice of coloured noises in stochastic dynamics of open quantum systems

AU - Matos, Daniel

AU - Lane, Matt

AU - Ford, Ian J.

AU - Kantorovich, Lev

PY - 2020/11/10

Y1 - 2020/11/10

N2 - The Stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quan- tum system reduced density matrix coupled to a non-Markovian harmonic environment. The in- teraction with the environment is represented by complex coloured noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating coloured noises of this kind that are built on a noise amplitude reduction procedure [H. Imai et al, Chemical Physics cbf446, 134 (2015)], including two analytically optimised schemes. In doing so, we pay close attention to the properties of the correlation func- tions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realisation that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well controlled method for doing so. We compare the ability of these schemes, along with an alternative optimised scheme [K. Schmitz and J. T. Stockburger, EPJ ST 227, 1929 (2019)], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimising an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.

AB - The Stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quan- tum system reduced density matrix coupled to a non-Markovian harmonic environment. The in- teraction with the environment is represented by complex coloured noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating coloured noises of this kind that are built on a noise amplitude reduction procedure [H. Imai et al, Chemical Physics cbf446, 134 (2015)], including two analytically optimised schemes. In doing so, we pay close attention to the properties of the correlation func- tions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realisation that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well controlled method for doing so. We compare the ability of these schemes, along with an alternative optimised scheme [K. Schmitz and J. T. Stockburger, EPJ ST 227, 1929 (2019)], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimising an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.

M3 - Article

SN - 1539-3755

JO - PHYSICAL REVIEW E

JF - PHYSICAL REVIEW E

ER -