# Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach

## Abstract

We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions for a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors.

- Authors:

- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853 (United States)

- Publication Date:

- OSTI Identifier:
- 22415758

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 18; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; CORRELATION FUNCTIONS; DEGREES OF FREEDOM; QUANTIZATION; QUANTUM MECHANICS; SEMICLASSICAL APPROXIMATION; TRANSFORMATIONS; TWO-DIMENSIONAL SYSTEMS

### Citation Formats

```
Antipov, Sergey V., Ye, Ziyu, and Ananth, Nandini, E-mail: ananth@cornell.edu.
```*Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach*. United States: N. p., 2015.
Web. doi:10.1063/1.4919667.

```
Antipov, Sergey V., Ye, Ziyu, & Ananth, Nandini, E-mail: ananth@cornell.edu.
```*Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach*. United States. doi:10.1063/1.4919667.

```
Antipov, Sergey V., Ye, Ziyu, and Ananth, Nandini, E-mail: ananth@cornell.edu. Thu .
"Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach". United States. doi:10.1063/1.4919667.
```

```
@article{osti_22415758,
```

title = {Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach},

author = {Antipov, Sergey V. and Ye, Ziyu and Ananth, Nandini, E-mail: ananth@cornell.edu},

abstractNote = {We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions for a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors.},

doi = {10.1063/1.4919667},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 18,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}