Approximating resonances with the Complex Absorbing Potential Method

Abstract

We study the Complex Absorbing Potential (CAP) Method in computing quantum resonances of width $c(h)=O(h^N)$, $N\gg 1$. We show that up to $h^{-M}\sqrt{c(h)} +\Oh$ error, $M\gg 1$, resonances are perturbed eigenvalues of the CAP Hamiltonian $P(h)-iW$, and vice versa, where $W$ is the CAP with non-negative real part supported outside the trapping region. In some cases, the error terms are exponentially small.

Cited by in corpus (1)

• Fractal upper bounds on the density of semiclassical resonances