# Electron-phonon interactions and recurrence phenomena in one-dimensional systems

## Abstract

We study the time dependence of a combined system of an electron described by a tight-binding model interacting with vibrational degrees of freedom in a one-dimensional lattice. The time evolution of our coupled model is described by a nonlinear system of differential-difference equations. Apart from localized solutions (polarons) and extended (Bloch-like) solutions, we found that for a small parameter range, there exists a periodic exchange of energy between the electronic and vibrational degrees of freedom: a small part of the electronic energy is transferred to the lattice and then completely back to the electron with an impressive regularity.

- Authors:

- Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)
- Research Center of Crete, P.O. Box 1527, 71110 Heraklion, Crete (Greece)

- Publication Date:

- Research Org.:
- Ames National Laboratory

- OSTI Identifier:
- 142620

- DOE Contract Number:
- W-7405-ENG-82

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, B: Condensed Matter

- Additional Journal Information:
- Journal Volume: 49; Journal Issue: 10; Other Information: PBD: 1 Mar 1994

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; ELECTRON-PHONON COUPLING; ONE-DIMENSIONAL CALCULATIONS; TIME DEPENDENCE; POLARONS; MANY-BODY PROBLEM; SCHROEDINGER EQUATION

### Citation Formats

```
Kopidakis, G., Soukoulis, C.M., and Economou, E.N..
```*Electron-phonon interactions and recurrence phenomena in one-dimensional systems*. United States: N. p., 1994.
Web. doi:10.1103/PhysRevB.49.7036.

```
Kopidakis, G., Soukoulis, C.M., & Economou, E.N..
```*Electron-phonon interactions and recurrence phenomena in one-dimensional systems*. United States. doi:10.1103/PhysRevB.49.7036.

```
Kopidakis, G., Soukoulis, C.M., and Economou, E.N.. Tue .
"Electron-phonon interactions and recurrence phenomena in one-dimensional systems". United States. doi:10.1103/PhysRevB.49.7036.
```

```
@article{osti_142620,
```

title = {Electron-phonon interactions and recurrence phenomena in one-dimensional systems},

author = {Kopidakis, G. and Soukoulis, C.M. and Economou, E.N.},

abstractNote = {We study the time dependence of a combined system of an electron described by a tight-binding model interacting with vibrational degrees of freedom in a one-dimensional lattice. The time evolution of our coupled model is described by a nonlinear system of differential-difference equations. Apart from localized solutions (polarons) and extended (Bloch-like) solutions, we found that for a small parameter range, there exists a periodic exchange of energy between the electronic and vibrational degrees of freedom: a small part of the electronic energy is transferred to the lattice and then completely back to the electron with an impressive regularity.},

doi = {10.1103/PhysRevB.49.7036},

journal = {Physical Review, B: Condensed Matter},

number = 10,

volume = 49,

place = {United States},

year = {1994},

month = {3}

}

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