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arXiv:2512.17207 · Physical Review A

Bound states and decay dynamics in $N$-level Friedrichs model with factorizable interactions

Jia-Ming Zhang, Yu Xin, Bing Chen

quant-phSubmitted Dec 19, 2025• Announced Dec 22, 2025• 0 citations
v1 · Dec 19, 2025v2 · Jul 28, 2026
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Abstract

Considering an $N$-level system interacting factorizably with a continuous spectrum, we derive analytical expressions for the bound states and the dynamical evolution within this single-excitation Friedrichs model by using the projection operator formalism. First, we establish explicit criteria to determine the number of bound states, whose existence suppresses the complete spontaneous decay of the system. Second, we derive the open system's dissipative dynamics, which is naturally described by an energy-independent non-Hermitian Hamiltonian in the Markovian limit. As an example, we apply our framework to an atomic chain embedded in a photonic crystal waveguide, uncovering a rich variety of decay dynamics and realizing an anti-$\mathcal{PT}$-symmetric Hamiltonian in the system's evolution.

Journal reference
Phys. Rev. A 114, 012214(2026)
DOI
10.1103/qvnj-zw99
Comments
27 pages, 5 figures

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