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

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung


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 nonzero 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 nonlinear variant of HOPS. In order to include nonzero-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.


Seiten (von - bis)5834-5845
FachzeitschriftJournal of Chemical Theory and Computation
PublikationsstatusVeröffentlicht - 2017

Externe IDs

Scopus 85038221015
ORCID /0000-0002-7806-3525/work/142234161
ORCID /0000-0002-8967-6183/work/142250860



  • Hierarchy of pure states, open systems, quantum dynamics, HOPS, spin boson model, numerical method, stochastic method, HOPS, Open Quantum System Dynamics