PMID- 35168335
OWN - NLM
STAT- PubMed-not-MEDLINE
LR  - 20220216
IS  - 1089-7690 (Electronic)
IS  - 0021-9606 (Linking)
VI  - 156
IP  - 6
DP  - 2022 Feb 14
TI  - A low-temperature quantum Fokker-Planck equation that improves the numerical 
      stability of the hierarchical equations of motion for the Brownian oscillator 
      spectral density.
PG  - 064107
LID - 10.1063/5.0082108 [doi]
AB  - We investigate the numerical stability of the hierarchical equations of motion 
      (HEOM) method applied to systems with the Brownian oscillator (BO) and multimode 
      BO (MBO) spectral densities. It is shown that, with the increase in the 
      system-bath coupling strength, the standard HEOM may become unstable, and a 
      simple increase in the truncation depth of the HEOM cannot remove the instability 
      at long times. To solve this problem, we first show that the high-temperature 
      approximation of the HEOM with the BO spectral density is equivalent to the 
      celebrated quantum Fokker-Planck equation (QFPE). By starting from the HEOM, we 
      then derive a new multidimensional phase space differential equation that 
      generalizes the QFPE to arbitrary temperature. It is further shown that the 
      numerical instability can be removed if the new low-temperature QFPE is expanded 
      in a basis set different than the one that leads to the conventional HEOM. The 
      matrix product state method is also employed to propagate the new equation based 
      on the low-temperature QFPE and to resolve the numerical instability problem for 
      an electron transfer model with the MBO spectral density presented in the recent 
      literature.
FAU - Li, Tianchu
AU  - Li T
AUID- ORCID: s0000000284842453
AD  - Beijing National Laboratory for Molecular Sciences, State Key Laboratory for 
      Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, 
      Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University 
      of Chinese Academy of Sciences, Beijing 100049, China.
FAU - Yan, Yaming
AU  - Yan Y
AUID- ORCID: s000000027622724X
AD  - Beijing National Laboratory for Molecular Sciences, State Key Laboratory for 
      Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, 
      Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University 
      of Chinese Academy of Sciences, Beijing 100049, China.
FAU - Shi, Qiang
AU  - Shi Q
AUID- ORCID: s0000000290462924
AD  - Beijing National Laboratory for Molecular Sciences, State Key Laboratory for 
      Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, 
      Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University 
      of Chinese Academy of Sciences, Beijing 100049, China.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - J Chem Phys
JT  - The Journal of chemical physics
JID - 0375360
SB  - IM
EDAT- 2022/02/17 06:00
MHDA- 2022/02/17 06:01
CRDT- 2022/02/16 05:33
PHST- 2022/02/16 05:33 [entrez]
PHST- 2022/02/17 06:00 [pubmed]
PHST- 2022/02/17 06:01 [medline]
AID - 10.1063/5.0082108 [doi]
PST - ppublish
SO  - J Chem Phys. 2022 Feb 14;156(6):064107. doi: 10.1063/5.0082108.