Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS)

Abstract

We show that the general and numerically exact Hierarchy of Pure States method (HOPS) is very well applicable to calculate the reduced dynamics of an open quantum system. In particular we focus on environments with a sub-Ohmic spectral density (SD) resulting in an algebraic decay of the bath correlation function (BCF). The universal applicability of HOPS, reaching from weak to strong coupling for zero and non-zero temperature, is demonstrated by solving the spin-boson model for which we find perfect agreement with other methods, each one suitable for a special regime of parameters. The challenges arising in the strong coupling regime are not only reflected in the computational effort needed for the HOPS method to converge but also in the necessity for an importance sampling mechanism, accounted for by the non-linear variant of HOPS. In order to include non-zero temperature effects in the strong coupling regime we found that it is highly favorable for the HOPS method to use the zero temperature BCF and include temperature via a stochastic Hermitian contribution to the system Hamiltonian.

Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

“…We call quantum trajectory the resulting joint self-consistent evolution of z and z b s b á Yñ | . It is worth noting that the outlined approach is similar in spirit to the non-Markovian quantum state diffusion methods [48,54,65] and to the modal interpretations of quantum mechanics [69,70]. However, the way we develop it, and the resulting description of non-Markovian dynamics, is quite different.…”

“…Thermal fluctuations as a classical noise In the most situations of interest, the open system is surrounded by a medium at a finite temperature. The idea of how to treat the finite temperature case was already discussed in the literature [48,63,64]. Suppose that the joint OQS-bath initial density matrix is a factorized one:…”

“…the memory function) decays only by the inverse power law [47]. This tail turns out to be important: whenever it is cut off (whether directly after a certain time cut t or indirectly by truncating N t ( )), a revival occurs after a finite time [48][49][50] so that the large-time asymptotical behavior of the observables is corrupted.…”

“…They propose an improvement for the finite memory cutoff approximation, which allows one to achieve converged results for certain parameter ranges of the superohmic model. There are also recent developments in the stochastic simulation algorithms [48,[54][55][56][57][58]. In particular, in [48] the hierarchy of pure states (HOPS) [54] method was applied to the case of subohmic bath.…”

“…There are also recent developments in the stochastic simulation algorithms [48,[54][55][56][57][58]. In particular, in [48] the hierarchy of pure states (HOPS) [54] method was applied to the case of subohmic bath. It is demonstrated that even if the absolute value of memory tail is very small, in the strong coupling regime its truncation considerably distorts the dynamics of observables.…”