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Bosonization for disordered and chaotic systems.

K B Efetov1, G Schwiete, K Takahashi

  • 1Theoretische Physik III, Ruhr-Universität Bochum, 44780 Bochum, Germany.

Physical Review Letters
|February 3, 2004
PubMed
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We developed a new supermatrix model for electron motion in external potentials. This exact model simplifies complex disordered and chaotic systems, offering a novel calculational approach for electron scattering.

Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Disordered systems

Background:

  • Electron motion in external potentials is complex, especially in disordered systems.
  • Existing nonlinear sigma models for disordered systems are often approximate.
  • A unified, exact model is needed for a comprehensive understanding.

Purpose of the Study:

  • To develop an exact supermatrix model for electron motion applicable at all distances.
  • To demonstrate the derivation of approximate models from this exact framework.
  • To apply the model to strong impurity scattering where approximations fail.

Main Methods:

  • Utilizing a supersymmetry formalism to reduce the electron motion problem.
  • Developing a novel supermatrix model.

Related Experiment Videos

  • Employing a coarse-graining procedure to derive approximate models.

    • Main Results:

    • An exact supermatrix model for electron motion in external potentials was established.
    • All previously obtained approximate nonlinear sigma models for disordered systems were derived from this exact model.
    • The approach was successfully applied to strong impurity scattering, avoiding the "mode-locking" problem.

    Conclusions:

    • The new supermatrix model offers an exact and versatile framework for studying disordered and chaotic systems.
    • This method provides a new calculational scheme for electron scattering, particularly in strong impurity regimes.
    • The formalism unifies various approximate models under a single exact theory.