2018/07/20 by Alexander Felski, S. P. Klevansky
Mathematics · Physics and Astronomy · #Analytic continuation #Computer science #Continuation #Eigenvalues and eigenvectors #Ground state #Harmonic #Harmonic oscillator #Mathematical analysis #Mathematics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Riemann hypothesis #Topological Materials and Phenomena #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreva.98.012127
published as Phys. Rev. A 98, 012127 (2018) · 11 pages, 7 figures
openalex publication_date 2018/07/20 · arxiv created 2018/08/15 · arxiv updated 2018/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By analytically continuing the eigenvalue problem of a system of two coupled harmonic oscillators in the complex coupling constant g, we have found a continuation structure through which the conventional ground state of the decoupled system is connected to three other lower unconventional ground states that describe the different combinations of the two constituent oscillators, taking all possible spectral phases of these oscillators into account [Bender et al., Phys. Scr. 92, 015201 (2017)]. In this work we calculate the connecting structures for the higher excitation states of the system and argue that, in contrast to the fourfold Riemann surface identified for the ground state, the general structure is eightfold instead. Furthermore we show that this structure in principle remains valid for equal oscillator frequencies as well and comment on the similarity of the connection structure to that of the single complex harmonic oscillator.