AharonovBohm Ring Touching a Quantum Wire: How to Model it and to Solve the Inverse Problem
Abstract
An explicitly solvable model of the gated AharonovBohm ring touching a quantum wire is constructed and investigated. The inverse spectral and scattering problems are discussed. It is shown that the TitchmarshWeyl matrix function associated with the boundary vertices determines a unique electric potential on the graph even though the graph contains a loop. This system gives another family of isospectral quantum graphs.
 Publication:

Reports on Mathematical Physics
 Pub Date:
 December 2011
 DOI:
 10.1016/S00344877(12)60010X
 Bibcode:
 2011RpMP...68..271K