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Interference in disordered systems: a particle in a complex random landscape.

Alexander Dobrinevski1, Pierre Le Doussal, Kay Jörg Wiese

  • 1CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, Paris, France. dobrinev@lpt.ens.fr

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Summary
This summary is machine-generated.

This study models particle behavior with disorder, revealing three distinct phases. Interference effects create universal forms and singularities in strong phase disorder, aiding higher-dimensional theory development.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Field Theory

Background:

  • Disorder and interference are crucial in condensed matter systems.
  • Existing models like Nguyen-Spivak-Shklovskii and Chalker-Coddington address conductivity and quantum Hall effects.
  • A simplified model is needed to study the interplay of disorder and interference.

Purpose of the Study:

  • To introduce a toy model for a particle in one dimension with amplitude and phase disorder.
  • To analyze the model's behavior and phase transitions.
  • To provide insights for developing field theories for higher-dimensional systems.

Main Methods:

  • Mapping the particle system to the complex Burgers equation.
  • Analytical computation of the renormalized disorder correlator.
  • Investigating interference effects and singularities.

Main Results:

  • Identification of three distinct phases: weak disorder, pinned (strong amplitude disorder), and diffusive (strong phase disorder).
  • Analytical calculation of the disorder correlator, showing a universal form in the diffusive phase.
  • Discovery of a logarithmic singularity due to interference in strong phase disorder.

Conclusions:

  • The complex Burgers equation serves as a valuable toy model for disorder-driven phenomena.
  • Interference effects lead to unique singularities, offering insights into complex system behavior.
  • The findings contribute to the search for adequate field theories for higher-dimensional disordered systems.