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Journal of Operator Theory

Volume 71, Issue 1, Winter 2014  pp. 259-283.

Complex absorbing potential method for Dirac operators. Clusters of resonances

Authors:  J. Kungsman (1) and M. Melgaard (2)
Author institution: (1) Department of Mathematics, Uppsala University, SE-751 06 Uppsala, Sweden
(2) Department of Mathematics, University of Sussex, Brighton BN1 9QH, Great Britain

Summary:  For both nonrelativistic and relativistic Hamiltonians, the complex absorbing potential (CAP) method has been applied extensively to calculate resonances in physics and chemistry. We study clusters of resonances for the perturbed Dirac operator near the real axis and, in the semiclassical limit, we establish the CAP method rigorously by showing that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa.

Keywords:  Dirac operator, resonances, semiclassical limit, complex distortion, quasi modes, complex absorbing potential, propagation of singularities.

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