Quantum Spring Picnic at Tosa Yamada, 2018
Speaker: Dr. Axel Perez-Obiol (Kochi Tech)
Title: Energy spectrum of the Non-linear Schrödinger equation on a ring with a defect computed automatically
Date & Time: March 15 (thu), 2018m 15:30-17:00 @
Place: room B504, Kami Campus, KUT
First I will show the reproduction of the first four energy levels (corresponding to stationary waves with real amplitude) of the non-linear 1D Schrödinger equation as computed by Nakamura and Cheon in Figs. 2-4 of [JPSJ 86 114001]. In my case, no gaps are found and all the energies are computed automatically. This energy spectrum will then be extended to the whole parameter space bounded by -5<g<5, -inf<t<inf, -1<v<1, where g is the non-linear parameter and t and v define the boundary conditions or defect. In order to automatize this computation, the eigenfunction, energy E, and integration parameters c, and x0 must be continuous in the parameter space (g,t,v). I will show how this is true if one uses a proper definition of the functions. At the end, I will comment a bit on scalability and complex eigenfunctions.