Resonances in a single-lead reflection from a disordered medium: σ-model approach

Yan V. Fyodorov*, Mikhail A. Skvortsov, Konstantin S. Tikhonov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Using the framework of supersymmetric non-linear σ-model we develop a general non-perturbative characterization of universal features of the density ρ(Γ) of the imaginary parts (“width”) for S-matrix poles (“resonances”) describing waves incident and reflected from a disordered medium via M-channel waveguide/lead. Explicit expressions for ρ(Γ) are derived for several instances of systems with broken time-reversal invariance, in particular for quasi-1D and 3D media. In the case of perfectly coupled lead with a few channels (M∼1) the most salient features are tails ρ(Γ)∼Γ−1 for narrow resonances reflecting exponential localization and ρ(Γ)∼Γ−2 for broad resonances reflecting states located in the vicinity of the attached wire. For multimode quasi 1D wires with M≫1, an intermediate asymptotics ρ(Γ)∼Γ−3/2 is shown to emerge reflecting diffusive nature of decay into wide enough contacts.

Original languageEnglish
Article number169568
Early online date7 Dec 2023
Publication statusPublished - Jan 2024


  • Anderson localization
  • Non-linear sigma model
  • Resonances


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