Improving the efficiency of hierarchical equations of motion approach and application to coherent dynamics in Aharonov-Bohm interferometers

The Journal of Chemical Physics
Dong HouYiJing Yan

Abstract

Several recent advancements for the hierarchical equations of motion (HEOM) approach are reported. First, we propose an a priori estimate for the optimal number of basis functions for the reservoir memory decomposition. Second, we make use of the sparsity of auxiliary density operators (ADOs) and propose two ansatzs to screen out all the intrinsic zero ADO elements. Third, we propose a new truncation scheme by utilizing the time derivatives of higher-tier ADOs. These novel techniques greatly reduce the memory cost of the HEOM approach, and thus enhance its efficiency and applicability. The improved HEOM approach is applied to simulate the coherent dynamics of Aharonov-Bohm double quantum dot interferometers. Quantitatively accurate dynamics is obtained for both noninteracting and interacting quantum dots. The crucial role of the quantum phase for the magnitude of quantum coherence and quantum entanglement is revealed.

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Dec 3, 2008·The Journal of Chemical Physics·Xiao ZhengYiJing Yan
May 2, 2009·The Journal of Chemical Physics·Qiang ShiYiJing Yan
May 2, 2009·The Journal of Chemical Physics·Xiao ZhengYiJing Yan
Sep 21, 2010·The Journal of Chemical Physics·Jie HuYijing Yan
Aug 21, 2013·The Journal of Chemical Physics·Jinshuang JinWei-Min Zhang
Sep 10, 2013·Physical Review Letters·Xiao ZhengMassimiliano Di Ventra
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Jul 6, 2014·The Journal of Chemical Physics·Jinshuang JinYiJing Yan
Sep 1, 2014·The Journal of Chemical Physics·Yu WangJinlong Yang

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Citations

Nov 18, 2015·Journal of Chemical Theory and Computation·Masashi Tsuchimoto, Yoshitaka Tanimura
Jun 22, 2015·The Journal of Chemical Physics·Jinshuang JinYiJing Yan
Dec 3, 2016·The Journal of Chemical Physics·Jin-Jin DingYiJing Yan
Jan 16, 2017·The Journal of Chemical Physics·Jin-Jin DingYiJing Yan
Jun 4, 2020·The Journal of Chemical Physics·Arif UllahVladimir Chernyak
Jun 4, 2020·The Journal of Chemical Physics·Lu HanVladimir Chernyak
Jun 25, 2018·The Journal of Chemical Physics·Lu HanYiJing Yan
Nov 18, 2015·Journal of Chemical Theory and Computation·David M Wilkins, Nikesh S Dattani

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