Flexible scheme to truncate the hierarchy of pure states

Abstract

The hierarchy of pure states (HOPS) is a wavefunction-based method which can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a 'good' truncation method, where by 'good' we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work we demonstrate the application of the '$n$-particle approximation' ($n$PA) to HOPS. We also introduce a new approximation, which we call the '$n$-mode approximation' ($n$MA). We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy. We show that truncation approximations can be used in combination to achieve convergence in two exemplary problems: absorption and energy transfer of molecular aggregates.

arXiv comment8 pages, 3 figures

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• Non-Markovian Quantum Dynamics in Strongly Coupled Multimode Cavities Conditioned on Continuous Measurement
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion
• Simulating optical linear absorption for mesoscale molecular aggregates: an adaptive hierarchy of pure states approach
• Simulation of absorption spectra of molecular aggregates: a Hierarchy of Stochastic Pure States approach
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• Non-Markovian Quantum State Diffusion for Spin Environments
• Environmentally Induced Entanglement -- Anomalous Behavior in the Adiabatic Regime
• Spectral signatures of the Markovian to Non-Markovian transition in open quantum systems
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions