Thermodynamic Quantum Time Crystals

Understand

Investigation of states with a periodic time dependence of physical quantities attracts a considerable interest now.

• Although it has been proposed initially that such states (coined Quantum Time Crystals) might be macroscopic and thermodynamically stable, results of a more careful study of the problem seemed to indicate that quantum time crystals could be realized only in systems out of equilibrium.
• Here we show that, in contrast to the general belief, thermodynamically stable macroscopic quantum time crystals can exist.
• The order parameter of this new state of matter is periodic in both real and imaginary time but its average over the phase of the oscillations equals zero.