Work

Scattering matrices for dissipative quantum systems

Year: 2018

Type: preprint

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{ö}dinger operator and spectral singularities correspond to real resonances.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1808.09179

Authors: Faupin, Jérémy, Nicoleau, Francois

Institutions: Institut Élie Cartan de Lorraine, Université de Lorraine, Laboratoire de Mathématiques Jean Leray, Université de Nantes, Nantes Université

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2950868759

Cites: 30

Cited by:

Related to: 20