Abstract:

Dirac operators with point interactions in one dimension and metric graphs are considered. Unlike Schrödinger operator the Dirac operator is not semi-bounded. In case of compact graphs the spectrum of Dirac operator is discrete and tends to both positive as well as negative infinity. For non-compact graphs the same operator has a continuous spectrum with a gap and covers (−∞, −𝑐² /2 )U(𝑐² /2 , ∞). The spectrum is discrete inside the gap. Our project focusses on the study of discrete spectrum of Dirac operator. We plan to investigate the problems of counting the number of eigenvalues within the gap and the estimating the positive eigenvalues in case of compact graphs.

Evaluation Committee   

• Dr. Muhammad Usman (Supervisor) 
• Dr. Ali Ashher Zaidi (Evaluator)