# Hierarchy of forward-backward stochastic Schrödinger equation

## Abstract

Driven by the impetus to simulate quantum dynamics in photosynthetic complexes or even larger molecular aggregates, we have established a hierarchy of forward-backward stochastic Schrödinger equation in the light of stochastic unravelling of the symmetric part of the influence functional in the path-integral formalism of reduced density operator. The method is numerically exact and is suited for Debye-Drude spectral density, Ohmic spectral density with an algebraic or exponential cutoff, as well as discrete vibrational modes. The power of this method is verified by performing the calculations of time-dependent population differences in the valuable spin-boson model from zero to high temperatures. By simulating excitation energy transfer dynamics of the realistic full FMO trimer, some important features are revealed.

- Authors:

- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005 (China)

- Publication Date:

- OSTI Identifier:
- 22675962

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 145; Journal Issue: 2; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ENERGY TRANSFER; PATH INTEGRALS; SCHROEDINGER EQUATION; SPECTRAL DENSITY; TEMPERATURE RANGE 0400-1000 K; TIME DEPENDENCE

### Citation Formats

```
Ke, Yaling, and Zhao, Yi, E-mail: yizhao@xmu.edu.cn.
```*Hierarchy of forward-backward stochastic Schrödinger equation*. United States: N. p., 2016.
Web. doi:10.1063/1.4955107.

```
Ke, Yaling, & Zhao, Yi, E-mail: yizhao@xmu.edu.cn.
```*Hierarchy of forward-backward stochastic Schrödinger equation*. United States. doi:10.1063/1.4955107.

```
Ke, Yaling, and Zhao, Yi, E-mail: yizhao@xmu.edu.cn. Thu .
"Hierarchy of forward-backward stochastic Schrödinger equation". United States. doi:10.1063/1.4955107.
```

```
@article{osti_22675962,
```

title = {Hierarchy of forward-backward stochastic Schrödinger equation},

author = {Ke, Yaling and Zhao, Yi, E-mail: yizhao@xmu.edu.cn},

abstractNote = {Driven by the impetus to simulate quantum dynamics in photosynthetic complexes or even larger molecular aggregates, we have established a hierarchy of forward-backward stochastic Schrödinger equation in the light of stochastic unravelling of the symmetric part of the influence functional in the path-integral formalism of reduced density operator. The method is numerically exact and is suited for Debye-Drude spectral density, Ohmic spectral density with an algebraic or exponential cutoff, as well as discrete vibrational modes. The power of this method is verified by performing the calculations of time-dependent population differences in the valuable spin-boson model from zero to high temperatures. By simulating excitation energy transfer dynamics of the realistic full FMO trimer, some important features are revealed.},

doi = {10.1063/1.4955107},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 2,

volume = 145,

place = {United States},

year = {2016},

month = {7}

}