Spectral properties of nonlinear Schrödinger equation on a ring
arXiv:1706.08695 · doi:10.7566/JPSJ.86.114001
Abstract
The stationary states of nonlinear Schr{ö}dinger equation on a ring with a defect is numerically analyzed. Unconventional connection conditions are imposed on the point defect, and it is shown that the system displays energy level crossings and level shifts and associated quantum holonomies in the space of system parameters, just as in the corresponding linear system. In the space of nonlinearity parameter, on the other hand, the degeneracy occurs on a line, excluding the possibility of any anholonomies. In contrast to the linear case, existence of exotic phenomena such as disappearance of energy level and foam-like structure are confirmed.
arXiv commentLaTeX 13 pages 7 figures
References in corpus (12)
- A Free Particle on a Circle with Point Interaction
- Fast solitons on star graphs
- Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations
- Bifurcations of standing localized waves on periodic graphs
- Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory
- Band structure loops and multistability in cavity-QED
- New anatomy of quantum holonomy
- Potential-controlled filtering in quantum star graphs
- Threshold resonance and controlled filtering in quantum star graphs
- Exploring the growth of correlations in a quasi one-dimensional trapped Bose gas
- A Study of a Nonlinear Schrödinger Equation for Optical Fibers
- Dynamics of trapped interacting vortices in Bose-Einstein condensates: Role of breathing degree of freedom