2008/02/29 by E. M. Graefe, E M Graefe, U. Guenther +5 · 2 citations
Mathematics · Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #cond-mat.other #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/25/255206
published as J. Phys. A: Math. Theor. 41 (2008) 255206 · minor changes
openalex publication_date 2008/05/28 · arxiv created 2008/05/31 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study a non-Hermitian PT-symmetric generalization of an N-particle, two-mode Bose-Hubbard system, modeling for example a Bose-Einstein condensate in a double well potential coupled to a continuum via a sink in one of the wells and a source in the other. The effect of the interplay between the particle interaction and the non-Hermiticity on characteristic features of the spectrum is analyzed drawing special attention to the occurrence and unfolding of exceptional points (EPs). We find that for vanishing particle interaction there are only two EPs of order N+1 which under perturbation unfold either into [(N+1)/2] eigenvalue pairs (and in case of N+1 odd, into an additional zero-eigenvalue) or into eigenvalue triplets (third-order eigenvalue rings) and (N+1)\mod 3 single eigenvalues, depending on the direction of the perturbation in parameter space. This behavior is described analytically using perturbational techniques. More general EP unfoldings into eigenvalue rings up to (N+1)th order are indicated.