# Statistical mechanics of a discrete nonlinear system

## Abstract

Statistical mechanics of the discrete nonlinear Schroedinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T=infinity, we identify a phase transition, through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breather-like localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Director, Office of Science. Office of Advanced Scientific Computing Research. Mathematical, Information, and Computational Sciences Division (US)

- OSTI Identifier:
- 797822

- Report Number(s):
- LBNL-44277

Journal ID: ISSN 0031-9007; PRLTAO; R&D Project: K11503; TRN: US0201738

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 17; Other Information: Journal Publication Date: Apr. 24, 2000; PBD: 1 Sep 1999; Journal ID: ISSN 0031-9007

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONSTRUCTION; HAMILTONIANS; NONLINEAR PROBLEMS; PARTITION FUNCTIONS; SCHROEDINGER EQUATION; STATISTICAL MECHANICS

### Citation Formats

```
Rasmussen, K.O., Cretegny, T., Kevrekidis, P.G., and Gronbech-Jensen, Niels.
```*Statistical mechanics of a discrete nonlinear system*. United States: N. p., 1999.
Web.

```
Rasmussen, K.O., Cretegny, T., Kevrekidis, P.G., & Gronbech-Jensen, Niels.
```*Statistical mechanics of a discrete nonlinear system*. United States.

```
Rasmussen, K.O., Cretegny, T., Kevrekidis, P.G., and Gronbech-Jensen, Niels. Wed .
"Statistical mechanics of a discrete nonlinear system". United States.
```

```
@article{osti_797822,
```

title = {Statistical mechanics of a discrete nonlinear system},

author = {Rasmussen, K.O. and Cretegny, T. and Kevrekidis, P.G. and Gronbech-Jensen, Niels},

abstractNote = {Statistical mechanics of the discrete nonlinear Schroedinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T=infinity, we identify a phase transition, through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breather-like localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.},

doi = {},

journal = {Physical Review Letters},

issn = {0031-9007},

number = 17,

volume = 84,

place = {United States},

year = {1999},

month = {9}

}

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