Bosonization for disordered and chaotic systems

TL;DR

This paper introduces an exact supermatrix model for electron motion in disordered and chaotic systems, enabling derivation of approximate models and addressing complex scattering scenarios without common limitations.

Contribution

It presents a new supersymmetry-based supermatrix model that is exact and applicable at all distances, unifying and extending previous approximate approaches.

Findings

Derived all previous nonlinear sigma models from the exact supermatrix model.

Demonstrated the model's effectiveness for smooth disorder without mode-locking issues.

Provided a new method for analyzing scattering on strong impurities beyond the Born approximation.

Abstract

Using a supersymmetry formalism, we reduce exactly the problem of electron motion in an external potential to a new supermatrix model valid at all distances. All approximate nonlinear sigma models obtained previously for disordered systems can be derived from our exact model using a coarse-graining procedure. As an example, we consider a model for a smooth disorder and demonstrate that using our approach does not lead to a 'mode-locking' problem. As a new application, we consider scattering on strong impurities for which the Born approximation cannot be used. Our method provides a new calculational scheme for disordered and chaotic systems.