Floquet isospectrality of the zero potential for discrete periodic Schrdinger operators

Let =q1Zq2ZqdZ, with qjZ+ for each j {1, , d}, and denote by the discrete Laplacian on 2Zd. Using Macaulay2, we first numerically find complex-valued -periodic potentials V:ZdC such that the operators + V and are Floquet isospectral. We then use combinatorial methods to validate these numerical solutions.

Faust, M., Liu, W., Matos, R., Plute, J., Robinson, J., Tao, Y., Tran, E., & Zhuang, C.

Faust, Matthew||Liu, Wencai||Matos, Rodrigo||Plute, Jenna||Robinson, Jonah||Tao, Yichen||Tran, Ethan||Zhuang, Cindy

Floquet isospectrality of the zero potential for discrete periodic Schrdinger operators Academic Article