# Conductance distribution in the magnetic field

## TL;DR

This paper derives the conductance distribution near the Anderson transition under magnetic fields, showing that magnetic variation only affects quantitative aspects without qualitative changes, using a more rigorous approach based on the generalized DMPK equation.

## Contribution

It introduces a more rigorous derivation of conductance distribution in magnetic fields near the Anderson transition using the generalized DMPK equation.

## Key findings

- Magnetic field variations do not qualitatively change conductance distribution.
- The approach is more rigorous and accurate than previous methods.
- Distribution equations are similar to the zero-field case.

## Abstract

Using a modification of the Shapiro scaling approach, we derive the distribution of conductance in the magnetic field applicable in the vicinity of the Anderson transition. This distribution is described by the same equations as in the absence of a field. Variation of the magnetic field does not lead to any qualitative effects in the conductance distribution and only changes its quantitative characteristics, moving a position of the system in the three-parameter space. In contrast to the original Shapiro approach, the evolution equation for quasi-1D systems is established from the generalized DMPK equation, and not by a simple analogy with one-dimensional systems; as a result, the whole approach became more rigorous and accurate.