Higher order addition laws on Abelian varieties and the fractional quantum Hall effect

TL;DR

This paper develops higher order addition formulas for theta functions and applies them to better understand the fractional quantum Hall effect in multi-layer electron systems with periodic boundary conditions.

Contribution

It introduces general addition formulas for theta functions of any order and applies these to analyze the fractional quantum Hall effect in complex multi-layer systems.

Findings

Derived addition formulas for theta functions of arbitrary order.

Applied these formulas to model the fractional quantum Hall effect.

Enhanced theoretical understanding of multi-layer electron systems.

Abstract

Addition formulas for theta functions of arbitrary order are shown and applied to the theoretical understanding of the fractional quantum Hall effect in a multi-layer two-dimensional many-electron system under periodic conditions.