# Theoretical proposal for dual transformation between the Josephson effect and quantum phase slip in single junction systems and nanowires

## TL;DR

This paper proposes a theoretical framework for duality between the Josephson effect and quantum phase slip in single junctions and nanowires, providing a new perspective on their relationship within quantum field theory.

## Contribution

It introduces a generalized dual field theory method to analyze the duality between Josephson effect and quantum phase slip, validated within the Villain approximation.

## Key findings

- Established duality between Josephson effect and quantum phase slip
- Validated the method within the Villain approximation
- Provided a theoretical basis for dual transformations in quantum systems

## Abstract

A method was devised to construct a generalized dual field theory in the quantum field theory. As a simple example using this method, we examined the duality between coherent quantum phase slip and the Josephson effect in single junction systems and nanowires. The this method was proved to be reliable within the Villain approximation.