# Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

## Abstract

In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

- Authors:

- Department of Chemistry, Stanford University, Stanford, California 94305 (United States)
- Department of Physics, Stanford University, Stanford, California 94305 (United States)

- Publication Date:

- OSTI Identifier:
- 22416206

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ENERGY TRANSFER; EQUATIONS; HAMILTONIANS; MARKOV PROCESS; MEAN-FIELD THEORY; QUANTUM SYSTEMS; RELAXATION; VELOCITY

### Citation Formats

```
Kelly, Aaron, Markland, Thomas E., E-mail: tmarkland@stanford.edu, and Brackbill, Nora.
```*Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations*. United States: N. p., 2015.
Web. doi:10.1063/1.4913686.

```
Kelly, Aaron, Markland, Thomas E., E-mail: tmarkland@stanford.edu, & Brackbill, Nora.
```*Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations*. United States. doi:10.1063/1.4913686.

```
Kelly, Aaron, Markland, Thomas E., E-mail: tmarkland@stanford.edu, and Brackbill, Nora. Sat .
"Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations". United States.
doi:10.1063/1.4913686.
```

```
@article{osti_22416206,
```

title = {Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations},

author = {Kelly, Aaron and Markland, Thomas E., E-mail: tmarkland@stanford.edu and Brackbill, Nora},

abstractNote = {In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.},

doi = {10.1063/1.4913686},

journal = {Journal of Chemical Physics},

number = 9,

volume = 142,

place = {United States},

year = {Sat Mar 07 00:00:00 EST 2015},

month = {Sat Mar 07 00:00:00 EST 2015}

}