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arXiv · 1808.09179

Scattering matrices for dissipative quantum systems

Jérémy Faupin·Francois Nicoleau
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Abstract

We consider a quantum system S interacting with another system S and susceptible of being absorbed by S. The effective, dissipative dynamics of S is supposed to be generated by an abstract pseudo-Hamiltonian of the form H = H0 + V -- iC * C. The generator of the free dynamics, H0, is self-adjoint, V is symmetric and C is bounded. We study the scattering theory for the pair of operators (H, H0). We establish a representation formula for the scattering matrices and identify a necessary and sufficient condition to their invertibility. This condition rests on a suitable notion of spectral singularity. Our main application is the nuclear optical model, where H is a dissipative Schr{\"o}dinger operator and spectral singularities correspond to real resonances.

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BibTeXRIS

Jérémy Faupin, Francois Nicoleau. 2018-08-28. Scattering matrices for dissipative quantum systems. https://arxiv.org/abs/1808.09179

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