Off-Diagonal Long-Range Order: Meissner Effect and Flux Quantization

TL;DR

This paper provides a straightforward proof that off-diagonal long-range order in the reduced density matrix implies both the Meissner effect and magnetic flux quantization, highlighting their common origin in phase coherence.

Contribution

It offers an elementary proof linking off-diagonal long-range order to both the Meissner effect and flux quantization, clarifying their relationship.

Findings

Off-diagonal long-range order implies the Meissner effect.

Off-diagonal long-range order leads to magnetic flux quantization.

Phase coherence underpins both phenomena.

Abstract

There has been a proof by Sewell that the hypothesis of off-diagonal long-range order in the reduced density matrix $\rho _2$ implies the Meissner effect. We present in this note an elementary and straightforward proof that not only the Meissner effect but also the property of magnetic flux quantization follows from the hypothesis. It is explicitly shown that the two phenomena are closely related, and phase coherence is the origin for both.