2001/10/30 by Tai‐Peng Tsai, Horng‐Tzer Yau, Tsai, Tai-Peng +1 · 1 citation
Mathematics · Physics and Astronomy · #35Q40 #35Q55 #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.math-ph/0110037
openalex publication_date 2001/10/30 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We consider nonlinear Schr "odinger equations in R3. Assume that the\nlinear Hamiltonians have two bound states. For certain finite codimension\nsubset in the space of initial data, we construct solutions converging to the\nexcited states in both non-resonant and resonant cases. In the resonant case,\nthe linearized operators around the excited states are non-self adjoint\nperturbations to some linear Hamiltonians with embedded eigenvalues. Although\nself-adjoint perturbation turns embedded eigenvalues into resonances, this\nclass of non-self adjoint perturbations turn an embedded eigenvalue into two\neigenvalues with the distance to the continuous spectrum given to the leading\norder by the Fermi golden rule.\n