論文公開:リング上の非線形シュレディンガー方程式

中村孝明君のトリノ工科大留学の成果の一つ、リング上の非線形シュレディンガー方程式を扱った初論文が公開されました。

Spectral properties of nonlinear Schrodinger equation on a ring
by T. Nakamura and T. Cheon

Abstract
The stationary states of nonlinear Schr ̈odinger 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 corre- sponding 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.

論文はarXivの
https://arxiv.org/abs/1706.08695
で読めます。これから厳しい査読が待っているはずですが。