Analytical study of resonant transport of BoseEinstein condensates
Abstract
We study the stationary nonlinear Schroedinger equation, or GrossPitaevskii equation, for a onedimensional finite squarewell potential. By neglecting the meanfield 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 beaktobeak structures are observed for a repulsive meanfield 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 boundstate 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, D67653 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; BOSEEINSTEIN CONDENSATION; BOUND STATE; EIGENFUNCTIONS; EIGENSTATES; EIGENVALUES; MEANFIELD THEORY; NONLINEAR PROBLEMS; ONEDIMENSIONAL CALCULATIONS; OSCILLATIONS; QUANTUM MECHANICS; RESONANCE; SCHROEDINGER EQUATION; SQUAREWELL POTENTIAL; WAVE FUNCTIONS
Citation Formats
Rapedius, K., Witthaut, D., and Korsch, H. J.. Analytical study of resonant transport of BoseEinstein 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 BoseEinstein condensates. United States. doi:10.1103/PHYSREVA.73.0.
Rapedius, K., Witthaut, D., and Korsch, H. J.. Wed .
"Analytical study of resonant transport of BoseEinstein condensates". United States.
doi:10.1103/PHYSREVA.73.0.
@article{osti_20786966,
title = {Analytical study of resonant transport of BoseEinstein condensates},
author = {Rapedius, K. and Witthaut, D. and Korsch, H. J.},
abstractNote = {We study the stationary nonlinear Schroedinger equation, or GrossPitaevskii equation, for a onedimensional finite squarewell potential. By neglecting the meanfield 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 beaktobeak structures are observed for a repulsive meanfield 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 boundstate 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}
}

Under investigation in this paper is a nonlinear Schroedinger equation with an arbitrary linear timedependent potential, which governs the soliton dynamics in quasionedimensional BoseEinstein condensates (quasi1DBECs). With Painleve analysis method performed to this model, its integrability is firstly examined. Then, the distinct treatments based on the truncated Painleve expansion, respectively, give the bilinear form and the PainleveBaecklund transformation with a family of new exact solutions. Furthermore, via the computerized symbolic computation, a direct method is employed to easily and directly derive the exact analytical dark and brightsolitonic solutions. At last, of physical and experimental interests, these solutions are graphically discussedmore »

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