Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential

Details Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential

2008-09-16

arxiv.org/abs/0809.2748v1

J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 044005

Physics

Condensed Matter

Other Condensed Matter

21 pages, 14 figures

Scientific paper

10.1088/0953-4075/42/4/044005

The resonance states and the decay dynamics of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation are studied for a simple, however flexible model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the resonance states is discussed, as well as their dynamical stability properties. A discrete approximation using a biorthogonal basis is suggested which allows an accurate description even for only two basis states in terms of a nonlinear, nonhermitian matrix problem.

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