6 papers
Anderson localization on quantum graphs coded by elements of a subshift of finite type
Oleg Safronov
We study Schrödinger operators on quantum graphs where the number of edges between points is determined by orbits of a "shift of finite type". We prove Anderson localization for th…
Spectral theory of Schrödinger operators with potentials that are measures supported on
Oleg Safronov
We discuss spectral properties of the one-dimensional Schrödinger operator with a potential of the form . Our main result says that the absolutely continuous spect…
Discrete Spectrum of the Bilayer Graphene Operator
Siyu Gao, Oleg Safronov
We consider the graphene operator perturbed by a decaying potential , where is a coupling constant. We study the number of eigenvalues of the operator $D(t)=…
Lyapunov exponent for quantum graphs that are elements of a subshift of finite type
Oleg Safronov
We consider the Schrödinger operator on the quantum graph whose edges connect the points of . The numbers of the edges connecting two consecutive points and are…
Monotonicity of the set of zeros of the Lyapunov exponent with respect to shift embeddings
Oleg Safronov
We consider the discrete Schrödinger operators with potentials whose values are read along the orbits of a shift of finite type. We study a certain subset of the collection of ener…
Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law
Oleg Safronov
In the first part of the paper we consider the Schrödinger operator We discuss the relation between the behavior of at the infinity and the properties of…