Time crystals: can diamagnetic currents drive a charge density wave into rotation?

TL;DR

This paper examines whether diamagnetic currents can induce a rotating charge density wave in a superfluid ring, concluding that such currents cannot drive rotation due to cancellation effects.

Contribution

It provides a simple example demonstrating that diamagnetic currents do not cause rotation of a charge density wave in a superfluid ring, clarifying the mechanism involved.

Findings

Diamagnetic currents cannot drive CDW rotation due to cancellation.

A superfluid ring with a magnetic field develops a charge density wave.

Naive calculations suggest no rotation induced by diamagnetic currents.

Abstract

It has been argued recently that an inhomogeneous system could rotate spontaneously in its ground state - hence a 'time crystal' which is periodic in time. In this note we present a very simple example: a superfluid ring threaded by a magnetic field which develops a charge density wave (CDW). A naive calculation shows that diamagnetic currents cannot drive rotation of the CDW, with a clear picture of the cancellation mechanism.