Generalized nonpolynomial Schrodinger equations for matter waves under anisotropic transverse confinement
arXiv:0907.1248 · doi:10.1088/1751-8113/42/33/335205
Abstract
Starting from the three-dimensional Gross-Pitaevskii equation we derive a 1D generalized nonpolynomial Schrodinger equation, which describes the dynamics of Bose-Einstein condensates under the action of a generic potential in the longitudinal axial direction and of an anisotropic harmonic potential in the transverse radial direction. This equation reduces to the familiar 1D nonpolynomial Schrodinger equation [Phys. Rev. A 65, 043614 (2002)] in the case of isotropic transverse harmonic confinement. In addition, we show that if the longitudinal potential models a periodic optical lattice the 3D GPE can be mapped into a 1D generalized discrete nonpolynomial Schrodinger equation.
9 pages, 2 figures, to be published in Journal of Physics A: Math. Theor
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- Effective equations for matter-wave gap solitons in higher-order transversal states
- Effective dipole-dipole interactions in multilayered dipolar Bose-Einstein condensates
- Effective equations for repulsive quasi-1D BECs trapped with anharmonic transverse potentials
- Quasi-one-dimensional approximation for Bose-Einstein condensates transversely trapped by a funnel potential
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- Shock waves in a quasi one-dimensional Bose-Einstein condensate
- Mean-field regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher order interactions in one and two dimensions
- Soliton-phonon scattering problem in 1D nonlinear Schrödinger systems with general nonlinearity
- Accurate one-dimensional effective description of realistic matter-wave gap solitons
- Dark solitons in the unitary Bose gas
- Dynamics of antiproton plasma in a time-dependent harmonic trap
- Symmetry Breaking in Bose-Einstein Condensates Confined by a Funnel Potential