# New mixed quantum/semiclassical propagation method

## Abstract

The authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem of heavier atoms. The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem. This follows from recent work by one of them, showing how one can calculate corrections to approximate evolution schemes, even when the Hamiltonian that corresponds to these approximate schemes is unknown. Then, they take the limit in which the width of the frozen Gaussians approaches zero, which makes the corrections to the evolution of the quantum subsystem depend only on classical bath coordinates. The test calculations they present use low-dimensional systems, in which comparison to exact quantum dynamics is feasible.

- Authors:

- Department of Biophysics, Albert Einstein College of Medicine, New York 10461 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20991266

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 126; Journal Issue: 18; Other Information: DOI: 10.1063/1.2731779; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GAUSSIAN PROCESSES; HAMILTONIANS; QUANTUM MECHANICS; SCHROEDINGER EQUATION; SEMICLASSICAL APPROXIMATION

### Citation Formats

```
Antoniou, Dimitri, Gelman, David, Schwartz, Steven D., and Department of Biophysics, Albert Einstein College of Medicine, Bronx, New York 10461 and Department of Biochemistry, Albert Einstein College of Medicine, Bronx, New York 10461.
```*New mixed quantum/semiclassical propagation method*. United States: N. p., 2007.
Web. doi:10.1063/1.2731779.

```
Antoniou, Dimitri, Gelman, David, Schwartz, Steven D., & Department of Biophysics, Albert Einstein College of Medicine, Bronx, New York 10461 and Department of Biochemistry, Albert Einstein College of Medicine, Bronx, New York 10461.
```*New mixed quantum/semiclassical propagation method*. United States. doi:10.1063/1.2731779.

```
Antoniou, Dimitri, Gelman, David, Schwartz, Steven D., and Department of Biophysics, Albert Einstein College of Medicine, Bronx, New York 10461 and Department of Biochemistry, Albert Einstein College of Medicine, Bronx, New York 10461. Mon .
"New mixed quantum/semiclassical propagation method". United States.
doi:10.1063/1.2731779.
```

```
@article{osti_20991266,
```

title = {New mixed quantum/semiclassical propagation method},

author = {Antoniou, Dimitri and Gelman, David and Schwartz, Steven D. and Department of Biophysics, Albert Einstein College of Medicine, Bronx, New York 10461 and Department of Biochemistry, Albert Einstein College of Medicine, Bronx, New York 10461},

abstractNote = {The authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem of heavier atoms. The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem. This follows from recent work by one of them, showing how one can calculate corrections to approximate evolution schemes, even when the Hamiltonian that corresponds to these approximate schemes is unknown. Then, they take the limit in which the width of the frozen Gaussians approaches zero, which makes the corrections to the evolution of the quantum subsystem depend only on classical bath coordinates. The test calculations they present use low-dimensional systems, in which comparison to exact quantum dynamics is feasible.},

doi = {10.1063/1.2731779},

journal = {Journal of Chemical Physics},

number = 18,

volume = 126,

place = {United States},

year = {Mon May 14 00:00:00 EDT 2007},

month = {Mon May 14 00:00:00 EDT 2007}

}