Anderson localization in the nondiscrete maryland model

Spectral properties of multi-layered graphene in a magnetic field

“…The explicit expression for G 0 is well-known. It was obtained in [29]: G 0 ðr; r 0 ; fÞ ¼ Uðr; r 0 ÞF 1 ðr À r 0 ; fÞ ¼ Uðr; r 0 ÞF 2 ðr À r 0 ; fÞ;…”

“…Using the Krein formula (3), one obtains the explicit expression for the Green function G of the operator H (analogously to[29,31]): Gðr; r 0 ; fÞ ¼ G 0 ðr; r 0 ; fÞ À X c;c 0 2C Q ðfÞ À A ½ À1 c;c 0 G 0 ðr; c; fÞG 0 ðc 0 ; r 0 ; fÞ:…”

Point perturbation-invariant solutions of the Schrödinger equation with a magnetic field

“…In [3] it was proved that the family of functions {g,(z0) : 7 E r} forms a Riesz basis in the deficiency space Ker(S* -z0) of the operator 5' and that B,o has the form…”

“…A negative answer to this question was given in [2] (see also [3]), where a continual series of groups, of intermediate growth (between the power growth and the exponential growth), each of which belongs to the difference AG \ EG was constructed. Original article submitted July 5, 1996.…”

Localization on Quantum Graphs with Random Vertex Couplings

“…A reduction of continuous problems to discrete ones within the localization framework was exploited in numerous papers on Schrödinger operators with random or quasiperiodic point interactions, see e.g. [5,9,16,12,19,20], but, as we will see below, such a correspondence is particularly explicit and efficient for quantum graphs.…”