181 citations · 3.2k across the 184 of their papers we have counts for
115 papers · 1 filter
Magnetic square lattice with vertex coupling of a preferred orientation
Marzieh Baradaran, Pavel Exner, Jiří Lipovský
We analyze a square lattice graph in a magnetic field assuming that the vertex coupling is of a particular type violating the time reversal invariance. Calculating the spectrum num…
Spectral transition model with the general contact interaction
Pavel Exner, Jiří Lipovský
Using a technique introduced by Sergei Naboko, we analyze a generalization of the parameter-controlled model of spectral transition, originally proposed by Smilansky and Solomyak,…
Continuum limit of the lattice quantum graph Hamiltonian
Pavel Exner, Shu Nakamura, Yukihide Tadano
We consider the quantum graph Hamiltonian on the square lattice in Euclidean space, and we show that the spectrum of the Hamiltonian converges to the corresponding Schrödinger oper…
Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph
Emilia Blåsten, Pavel Exner, Hiroshi Isozaki +2
We consider the inverse scattering problems for two types of Schrödinger operators on locally perturbed periodic lattices. For the discrete Hamiltonian, the knowledge of the S-matr…
Magnetic ring chains with vertex coupling of a preferred orientation
Marzieh Baradaran, Pavel Exner, Jiri Lipovsky
We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex cou…
Quantum graphs: self-adjoint, and yet exhibiting a nontrivial -symmetry
Pavel Exner, Milos Tater
We demonstrate that a quantum graph exhibits a -symmetry provided the coefficients in the condition describing the wave function matching at the vertices are circulan…