Meissner State in Classical Ideal Charged Fluid

TL;DR

This paper demonstrates that a classical ideal charged fluid model can exhibit the Meissner state with correct penetration depth, highlighting key differences from traditional models and similarities to quantum models.

Contribution

It introduces a classical charged fluid model that successfully predicts the Meissner effect, emphasizing the importance of pressure and velocity terms often neglected in classical approaches.

Findings

The model exhibits the Meissner state with correct penetration depth.

Differences from traditional classical models are discussed.

Similarities to the coupled Schrödinger-Maxwell model are identified.

Abstract

It is shown that a model of a superconductor as a classical ideal charged fluid at constant uniform temperature in a uniform compensating positively charged background exhibits the Meissner state with the correct value of the penetration depth. The differences between this model and the textbook classical model that fails to predict the Meissner state are discussed, as are the similarities of this model to the coupled Schrodinger-Maxwell model, which does predict flux exclusion. In particular, this model does not neglect the pressure term and terms that are bilinear in the velocity in the fluid equations; these terms are essential to the results.