Non-Stationary Quantum Systems Associated with Stationary Scattering in One Dimension

Abstract:Stationary scattering admits a dynamical formulation in which the scattering data are extracted from the evolution operator for an effective non-stationary and non-unitary quantum system. This provides a mathematical method of solving scattering problems. We consider the possibility of realizing such a quantum system and relating the scattering information to outcomes of quantum measurements performed on it. To this end, we examine stationary scattering problems in one dimension where the scattering data consist of reflection and transmission amplitudes and the corresponding effective quantum system is a non-unitary two-level system. The states of this system identify points in a Bloch sphere $S^2$ and their evolution yields trajectories in $S^2$. Quantum measurements turn out to be capable of providing information about the reflection amplitudes. We identify configurations displaying reflectionlessness with situations where one or both of the poles of $S^2$ undergo cyclic evolutions. Spectral singularities and coherent perfect absorption correspond to dynamical spin flips which map one of the poles of $S^2$ to the other.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Optics (physics.optics)

arXiv:2610.15655 [quant-ph]

(or arXiv:2610.15655v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.15655 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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