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Non-Hermitian impurity problem.

Emmanouil T Kokkinakis1,2, Ioannis Komis1,2, Konstantinos G Makris1,2

  • 1Department of Physics, University of Crete, Heraklion, Greece.

Communications Physics
|May 4, 2026
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Summary
This summary is machine-generated.

This study explores the non-Hermitian single impurity problem in condensed matter physics. We found novel localization phenomena and exotic states in finite lattices, relevant for photonic platforms.

Keywords:
Condensed-matter physicsOptics and photonics

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Materials science

Background:

  • The single Hermitian impurity problem is key to understanding Anderson localization.
  • Non-Hermitian lattices with defects are gaining interest, but the impurity problem is underexplored.
  • Understanding localization in non-Hermitian systems is crucial for novel quantum devices.

Purpose of the Study:

  • Investigate the role of a single complex impurity in various dimensional tight-binding lattices.
  • Explore spectral and localization properties in non-Hermitian systems.
  • Analyze finite-sized lattices for experimental relevance in photonic platforms.

Main Methods:

  • Theoretical investigation of complex impurities in 1D, 2D, and 3D tight-binding lattices.
  • Analysis of both infinite and finite lattice structures.
  • Characterization of localized states and eigenstates.

Main Results:

  • Observed counterintuitive phenomena: vanishing and re-emerging localization with impurity strength.
  • Discovered scale-free localized states and peculiar cross-shaped eigenstates in finite lattices.
  • Deviations from conventional exponential localization profiles were identified.

Conclusions:

  • The non-Hermitian single impurity problem exhibits unique behaviors distinct from Hermitian systems.
  • Exotic localized states in finite lattices offer new avenues for experimental exploration.
  • This research provides a foundation for studying transport in non-Hermitian disordered systems.