# Nonequilibrium approach to Bloch-Peierls-Berry dynamics

## Abstract

We examine Bloch-Peierls-Berry dynamics under a classical nonequilibrium dynamical formulation. In this formulation all coordinates in phase space formed by the position and crystal-momentum space are treated on an equal footing. Explicit demonstrations of no (naive) Liouville theorem and of the validity of the Darboux theorem are given. Regardless, the explicit equilibrium-distribution function is obtained. Similarities and differences to previous approaches are discussed, and in particular, an interesting singular situation becomes nonsingular in the presence of dissipation. Our results confirm the richness of Bloch-Peierls-Berry dynamics.

- Authors:

- Mechanical Engineering Department, University of Washington, Seattle, Washington 98195 (United States)

- Publication Date:

- OSTI Identifier:
- 20976654

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevB.75.035114; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN-VLASOV EQUATION; COORDINATES; CRYSTALS; DISTRIBUTION FUNCTIONS; DYNAMICS; EQUILIBRIUM; LIOUVILLE THEOREM; PHASE SPACE

### Citation Formats

```
Olson, John C., and Ao Ping.
```*Nonequilibrium approach to Bloch-Peierls-Berry dynamics*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVB.75.035114.

```
Olson, John C., & Ao Ping.
```*Nonequilibrium approach to Bloch-Peierls-Berry dynamics*. United States. doi:10.1103/PHYSREVB.75.035114.

```
Olson, John C., and Ao Ping. Mon .
"Nonequilibrium approach to Bloch-Peierls-Berry dynamics". United States.
doi:10.1103/PHYSREVB.75.035114.
```

```
@article{osti_20976654,
```

title = {Nonequilibrium approach to Bloch-Peierls-Berry dynamics},

author = {Olson, John C. and Ao Ping},

abstractNote = {We examine Bloch-Peierls-Berry dynamics under a classical nonequilibrium dynamical formulation. In this formulation all coordinates in phase space formed by the position and crystal-momentum space are treated on an equal footing. Explicit demonstrations of no (naive) Liouville theorem and of the validity of the Darboux theorem are given. Regardless, the explicit equilibrium-distribution function is obtained. Similarities and differences to previous approaches are discussed, and in particular, an interesting singular situation becomes nonsingular in the presence of dissipation. Our results confirm the richness of Bloch-Peierls-Berry dynamics.},

doi = {10.1103/PHYSREVB.75.035114},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 3,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}

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