# Analytical study of resonant transport of Bose-Einstein condensates

## Abstract

We study the stationary nonlinear Schroedinger equation, or Gross-Pitaevskii equation, for a one-dimensional finite square-well potential. By neglecting the mean-field interaction outside the potential well it is possible to discuss the transport properties of the system analytically in terms of ingoing and outgoing waves. Resonances and bound states are obtained analytically. The transmitted flux shows a bistable behavior. Novel crossing scenarios of eigenstates similar to beak-to-beak structures are observed for a repulsive mean-field interaction. It is proven that resonances transform to bound states due to an attractive nonlinearity and vice versa for a repulsive nonlinearity, and the critical nonlinearity for the transformation is calculated analytically. The bound-state wave functions of the system satisfy an oscillation theorem as in the case of linear quantum mechanics. Furthermore, the implications of the eigenstates on the dymamics of the system are discussed.

- Authors:

- Technische Universitaet Kaiserslautern, FB Physik, D-67653 Kaiserslautern (Germany)

- Publication Date:

- OSTI Identifier:
- 20786966

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.033608; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; BOSE-EINSTEIN CONDENSATION; BOUND STATE; EIGENFUNCTIONS; EIGENSTATES; EIGENVALUES; MEAN-FIELD THEORY; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; OSCILLATIONS; QUANTUM MECHANICS; RESONANCE; SCHROEDINGER EQUATION; SQUARE-WELL POTENTIAL; WAVE FUNCTIONS

### Citation Formats

```
Rapedius, K., Witthaut, D., and Korsch, H. J..
```*Analytical study of resonant transport of Bose-Einstein condensates*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Rapedius, K., Witthaut, D., & Korsch, H. J..
```*Analytical study of resonant transport of Bose-Einstein condensates*. United States. doi:10.1103/PHYSREVA.73.0.

```
Rapedius, K., Witthaut, D., and Korsch, H. J.. Wed .
"Analytical study of resonant transport of Bose-Einstein condensates". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20786966,
```

title = {Analytical study of resonant transport of Bose-Einstein condensates},

author = {Rapedius, K. and Witthaut, D. and Korsch, H. J.},

abstractNote = {We study the stationary nonlinear Schroedinger equation, or Gross-Pitaevskii equation, for a one-dimensional finite square-well potential. By neglecting the mean-field interaction outside the potential well it is possible to discuss the transport properties of the system analytically in terms of ingoing and outgoing waves. Resonances and bound states are obtained analytically. The transmitted flux shows a bistable behavior. Novel crossing scenarios of eigenstates similar to beak-to-beak structures are observed for a repulsive mean-field interaction. It is proven that resonances transform to bound states due to an attractive nonlinearity and vice versa for a repulsive nonlinearity, and the critical nonlinearity for the transformation is calculated analytically. The bound-state wave functions of the system satisfy an oscillation theorem as in the case of linear quantum mechanics. Furthermore, the implications of the eigenstates on the dymamics of the system are discussed.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 3,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}