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math.SP2026
Periodic discrete graphs with prescribed spectrum
Andrii Khrabustovskyi, Anna Muranova
We construct a periodic weighted graph whose discrete Laplacian has a spectrum with precisely gaps. Moreover, we show that by an appropriate choice of the weights, the endpoint…
math.SP2024
Quantum lattice transport along an infinitely extended perturbation
Marzieh Baradaran, Pavel Exner, Andrii Khrabustovskyi
We consider a periodic quantum graph in the form of a rectangular lattice with the -coupling of strength in the vertices perturbed by changing the latter at an infinite st…