WavePacket: A Matlab package for numerical quantum dynamics. II: Open quantum systems, optimal control, and model reduction

摘要

WavePacket is an open-source program package for numeric simulations inquantum dynamics. It can solve time-independent or time-dependent linearSchr\"odinger and Liouville-von Neumann-equations in one or more dimensions.Also coupled equations can be treated, which allows, e.g., to simulatemolecular quantum dynamics beyond the Born-Oppenheimer approximation.Optionally accounting for the interaction with external electric fields withinthe semi-classical dipole approximation, WavePacket can be used to simulateexperiments involving tailored light pulses in photo-induced physics orchemistry. Being highly versatile and offering visualization of quantumdynamics 'on the fly', WavePacket is well suited for teaching or researchprojects in atomic, molecular and optical physics as well as in physical ortheoretical chemistry. Building on the previous Part I which dealt with closedquantum systems and discrete variable representations, the present Part IIfocuses on the dynamics of open quantum systems, with Lindblad operatorsmodeling dissipation and dephasing. This part also describes the WavePacketfunction for optimal control of quantum dynamics, building on rapidmonotonically convergent iteration methods. Furthermore, two differentapproaches to dimension reduction implemented in WavePacket are documentedhere. In the first one, a balancing transformation based on the concepts ofcontrollability and observability Gramians is used to identify states that areneither well controllable nor well observable. Those states are eithertruncated or averaged out. In the other approach, the H2-error for a givenreduced dimensionality is minimized by H2 optimal model reduction techniques,utilizing a bilinear iterative rational Krylov algorithm.