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PreprintarXiv licencearXiv

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

  • Ali Mostafazadeh
  • Alireza Shariati Joni
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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 S2 and their evolution yields trajectories in S2. 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 S2 undergo cyclic evolutions. Spectral singularities and coherent perfect absorption correspond to dynamical spin flips which map one of the poles of S2 to the other.

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Cite

BibTeXRIS
BibTeX
@misc{mostafazadeh2026nonstationary,
  title = {{Non-Stationary Quantum Systems Associated with Stationary Scattering in One Dimension}},
  author = {Ali Mostafazadeh and Alireza Shariati Joni},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15655},
  eprint = {2610.15655},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15655},
}
RIS
TY  - UNPB
TI  - Non-Stationary Quantum Systems Associated with Stationary Scattering in One Dimension
AU  - Ali Mostafazadeh
AU  - Alireza Shariati Joni
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15655
UR  - https://arxiv.org/abs/2610.15655
AB  - 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.
ER  -