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Localization-delocalization transition in non-hermitian disordered systems

Kolesnikov1, Efetov

  • 1Fakultat fur Physik und Astronomie, Ruhr-Universitat, Bochum, Universitatsstrasse 150, Bochum, Germany.

Physical Review Letters
|September 16, 2000
PubMed
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This study investigates the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems. The research reveals an abrupt transition driven by the interplay of two saddle points in the free energy functional.

Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Physics

Background:

  • Non-Hermitian systems exhibit unique properties due to their complex energy spectra.
  • Understanding localization-delocalization transitions is crucial for characterizing transport phenomena in disordered systems.

Purpose of the Study:

  • To investigate the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a defined direction.
  • To analyze the diffusive character of carrier motion at short distances, contrasting with simpler chain models.

Main Methods:

  • Application of the supersymmetry technique.
  • Calculation of the joint probability of complex eigenvalues.
  • Analysis of relevant correlation functions.

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Main Results:

  • The study captures the diffusive nature of carrier motion at short distances.
  • An abrupt localization-delocalization transition was identified.
  • The transition is attributed to the interplay between two saddle points in the free energy functional.

Conclusions:

  • The supersymmetry technique provides a powerful framework for studying complex phenomena in non-Hermitian systems.
  • The identified abrupt transition mechanism offers new insights into transport properties in these systems.