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Scattering states in one-dimensional non-Hermitian baths

Jimin Li1, Yuwen E. Zhang2, Franco Nori3,4,5, and Zongping Gong6

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Phys. Rev. A 112, 053707 – Published 10 November, 2025

DOI: https://doi.org/10.1103/gzpw-4c74

Abstract

A single quantum emitter coupled to a structured non-Hermitian environment shows anomalous bound states and real-time dynamics without Hermitian counterparts, as shown in Gong et al. [Phys. Rev. Lett. 129, 223601 (2022)]. In this work, we establish a general approach for studying the scattering states of a single quantum emitter coupled to one-dimensional non-Hermitian single-band baths. We formally solve the exact eigenvalue equation for all the scattering states defined on finite periodic lattices. In the thermodynamic limit, the formal solution reduces to the celebrated Lippmann-Schwinger equation for generic baths. In this case, we find that the scattering states are no longer linear superpositions of plane waves in general, unlike those in Hermitian systems; instead, the wave functions exhibit a large, yet finite localization length proportional to the lattice size. Furthermore, we show and discuss the cases where the Lippmann-Schwinger equation breaks down. We find the analytical solutions for the Hatano-Nelson and unidirectional next-to-nearest-neighbor baths in the thermodynamic limit.

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Phys. Rev. A 112, 053707– Published 10 November, 2025
  • Received 16 July 2025
  • Accepted 15 October 2025
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