Research conducted by the group of Prof. Walter Strunz (Institute of Theoretical Physics, TU Dresden University of Technology, 01062 Dresden, Germany)
The Hierarchy of Pure States (HOPS) is a stochastic numerical method to rigorously solve the full Schrödinger Equation for the system and its environment in a Monte-Carlo sense [1,2]. It is based on the stochastic pure state formalism governed by the Non-Markovian Quantum State Diffusion (NMQSD) equation [3], now reformulated in a hierarchical scheme (similar to HEOM [4], a density matrix based approach to the same problem). In contrast to many "reduced" approaches (e.g. master equation techniques), no approximations on the level of the global Hamiltonian are required. The method is exact in the sense that numerical errors can be made arbitrarily small, in a controlled way. Details of HOPS have been discussed in Ref. [2,5,6]
A utility to accurately sample complex-valued stationary Gaussian stochastic processes continuously in time for a given auto-correlation-functions.
