From ODLRO to the Meissner Effect and Flux Quantization

TL;DR

This paper extends the understanding of off-diagonal long-range order (ODLRO) in electron systems, demonstrating that such systems cannot support non-uniform magnetic fields and that magnetic flux trapped is quantized, reinforcing the connection to superconductivity phenomena.

Contribution

It generalizes previous results by showing ODLRO systems cannot support non-uniform or slowly varying magnetic fields, and confirms flux quantization in these systems.

Findings

ODLRO systems cannot support non-uniform magnetic fields.

Magnetic flux trapped in ODLRO systems is quantized.

Supports the link between ODLRO and superconductivity phenomena.

Abstract

It has been shown that the electron system with ODLRO in the reduced density matrix $\rho _2$ can not support a uniform magnetic field, i.e., ODLRO\ in $% \rho _2$ implies the Meissner effect \cite{2}\cite{3}, furthermore, the magnetic field trapped in the system is quantized\cite{3}. This note extends above results in two cases. We show that (1) the system with ODLRO in $\rho _2$ can not support a non uniform, cylindrically symmetric magnetic field; (2) the system with ODLRO in $\rho _2$ can not support a magnetic field slowly varying in space, and the magnetic flux trapped in it is quantized.