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

Abstract

The resonance states and the decay dynamics of the nonlinear Schrödinger (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.

21 pages, 14 figures

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Cited by in corpus (11)

• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• Exceptional points in the spectra of atoms in external fields
• Coupling approach for the realization of a $\mathcal{P}\mathcal{T}$-symmetric potential for a Bose-Einstein condensate in a double well
• Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices
• Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates
• Calculating resonance positions and widths using the Siegert approximation method
• Interaction-induced decoherence in non-Hermitian quantum walks of ultracold Bosons
• Matter-wave scattering on a BEC in a double-well potential
• Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates