Impossibility of Spontaneously Rotating Time-Crystals: A No-Go Theorem

TL;DR

This paper proves a no-go theorem demonstrating that spontaneously rotating quantum time-crystals cannot exist in ground states or thermal equilibrium, challenging recent proposals of such phenomena.

Contribution

It provides a rigorous proof ruling out the possibility of spontaneous rotation in quantum time-crystals in equilibrium states.

Findings

Spontaneous rotation in quantum time-crystals is impossible in ground states.

The no-go theorem applies to a broad class of systems.

The results challenge recent claims of spontaneously rotating time-crystals.

Abstract

I present arguments indicating the impossibility of spontaneously rotating quantum timecrystals, as recently proposed by Frank Wilczek [arXiv:1202.2539]. In particular, I prove a No-Go Theorem, rigorously ruling out the possibility of spontaneous ground-state (or thermal equilibrium) rotation for a broad class of systems.