PMID- 31255062
OWN - NLM
STAT- PubMed-not-MEDLINE
LR  - 20190701
IS  - 1089-7690 (Electronic)
IS  - 0021-9606 (Linking)
VI  - 150
IP  - 24
DP  - 2019 Jun 28
TI  - Chebyshev hierarchical equations of motion for systems with arbitrary spectral 
      densities and temperatures.
PG  - 244104
LID - 10.1063/1.5100102 [doi]
AB  - The time evolution in open quantum systems, such as a molecular aggregate in 
      contact with a thermal bath, still poses a complex and challenging problem. The 
      influence of the thermal noise can be treated using a plethora of schemes, 
      several of which decompose the corresponding correlation functions in terms of 
      weighted sums of exponential functions. One such scheme is based on the 
      hierarchical equations of motion (HEOM), which is built using only certain forms 
      of bath correlation functions. In the case where the environment is described by 
      a complex spectral density or is at a very low temperature, approaches utilizing 
      the exponential decomposition become very inefficient. Here, we utilize an 
      alternative decomposition scheme for the bath correlation function based on 
      Chebyshev polynomials and Bessel functions to derive a HEOM approach up to an 
      arbitrary order in the environmental coupling. These hierarchical equations are 
      similar in structure to the popular exponential HEOM scheme, but are formulated 
      using the derivatives of the Bessel functions. The proposed scheme is tested up 
      to the fourth order in perturbation theory for a two-level system and compared to 
      benchmark calculations for the case of zero-temperature quantum Ohmic and 
      super-Ohmic noise. Furthermore, the benefits and shortcomings of the present 
      Chebyshev-based hierarchical equations are discussed.
FAU - Rahman, Hasan
AU  - Rahman H
AD  - Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 
      1, 28759 Bremen, Germany.
FAU - Kleinekathofer, Ulrich
AU  - Kleinekathofer U
AUID- ORCID: 0000000261147431
AD  - Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 
      1, 28759 Bremen, Germany.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - J Chem Phys
JT  - The Journal of chemical physics
JID - 0375360
EDAT- 2019/07/01 06:00
MHDA- 2019/07/01 06:01
CRDT- 2019/07/01 06:00
PHST- 2019/07/01 06:00 [entrez]
PHST- 2019/07/01 06:00 [pubmed]
PHST- 2019/07/01 06:01 [medline]
AID - 10.1063/1.5100102 [doi]
PST - ppublish
SO  - J Chem Phys. 2019 Jun 28;150(24):244104. doi: 10.1063/1.5100102.