PMID- 31091920
OWN - NLM
STAT- PubMed-not-MEDLINE
LR  - 20191120
IS  - 1089-7690 (Electronic)
IS  - 0021-9606 (Linking)
VI  - 150
IP  - 18
DP  - 2019 May 14
TI  - Removing instabilities in the hierarchical equations of motion: Exact and 
      approximate projection approaches.
PG  - 184109
LID - 10.1063/1.5092616 [doi]
AB  - The hierarchical equations of motion (HEOM) provide a numerically exact approach 
      for computing the reduced dynamics of a quantum system linearly coupled to a 
      bath. We have found that HEOM contains temperature-dependent instabilities that 
      grow exponentially in time. In the case of continuous-bath models, these 
      instabilities may be delayed to later times by increasing the hierarchy 
      dimension; however, for systems coupled to discrete, nondispersive modes, 
      increasing the hierarchy dimension does little to alleviate the problem. We show 
      that these instabilities can also be removed completely at a potentially much 
      lower cost via projection onto the space of stable eigenmodes; furthermore, we 
      find that for discrete-bath models at zero temperature, the remaining projected 
      dynamics computed with few hierarchy levels are essentially identical to the 
      exact dynamics that otherwise might require an intractably large number of 
      hierarchy levels for convergence. Recognizing that computation of the eigenmodes 
      might be prohibitive, e.g., for large or strongly coupled models, we present a 
      Prony filtration algorithm that may be useful as an alternative for accomplishing 
      this projection when diagonalization is too costly. We present results 
      demonstrating the efficacy of HEOM projected via diagonalization and Prony 
      filtration. We also discuss issues associated with the non-normality of HEOM.
FAU - Dunn, Ian S
AU  - Dunn IS
AUID- ORCID: 0000000287731580
AD  - Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 
      10027, USA.
FAU - Tempelaar, Roel
AU  - Tempelaar R
AUID- ORCID: 0000000307867304
AD  - Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 
      10027, USA.
FAU - Reichman, David R
AU  - Reichman DR
AUID- ORCID: 0000000252655637
AD  - Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 
      10027, USA.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - J Chem Phys
JT  - The Journal of chemical physics
JID - 0375360
EDAT- 2019/05/17 06:00
MHDA- 2019/05/17 06:01
CRDT- 2019/05/17 06:00
PHST- 2019/05/17 06:00 [entrez]
PHST- 2019/05/17 06:00 [pubmed]
PHST- 2019/05/17 06:01 [medline]
AID - 10.1063/1.5092616 [doi]
PST - ppublish
SO  - J Chem Phys. 2019 May 14;150(18):184109. doi: 10.1063/1.5092616.