{
  "id": "2211.03376",
  "version": "v1",
  "published": "2022-11-07T09:15:51.000Z",
  "updated": "2022-11-07T09:15:51.000Z",
  "title": "Resonances in a single-lead reflection from a disordered medium: $σ$-model approach",
  "authors": [
    "Yan V. Fyodorov",
    "Mikhail A. Skvortsov",
    "Konstantin S. Tikhonov"
  ],
  "comment": "Article+Supplemental Material",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.mes-hall",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We develop a general non-perturbative characterisation of universal features of the density $\\rho(\\Gamma)$ of $S$-matrix poles (resonances) $E_n-i\\Gamma_n$ describing waves incident and reflected from a disordered medium via a single $M$-channel waveguide/lead. Explicit expressions for $\\rho(\\Gamma)$ 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 ($M\\sim 1$) the most salient features are tails $\\rho(\\Gamma)\\sim 1/\\Gamma$ for narrow resonances reflecting exponential localization and $\\rho(\\Gamma)\\sim 1/\\Gamma^2$ for broad resonances reflecting states located in the vicinity of the attached wire. For multimode wires with $M\\gg 1$, intermediate asymptotics $\\rho(\\Gamma)\\sim 1/\\Gamma^{3/2}$ is shown to emerge reflecting diffusive nature of decay into wide enough contacts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-07T09:15:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "disordered medium",
      "model approach",
      "single-lead reflection",
      "narrow resonances reflecting exponential localization",
      "broad resonances reflecting states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}