Abstract
Out-of-equilibrium states in glasses and crystals have been a major topic of research in condensed-matter physics for many years, and the idea of time crystals has triggered a flurry of new research. Here, we provide a description for the recently conjectured time glasses using fractional calculus methods. An exactly solvable effective theory is introduced with a continuous parameter describing the transition from liquid through normal glass and time glass into the Gardner phase. The phenomenological description with a fractional Langevin equation is connected to a microscopic model of a particle in a sub-Ohmic bath in the framework of a generalized Caldeira-Leggett model.
| Original language | English |
|---|---|
| Article number | L180301 |
| Number of pages | 6 |
| Journal | Physical Review B |
| Volume | 103 |
| Issue number | 18 |
| DOIs | |
| Publication status | Published - 1 May 2021 |
Bibliographical note
Funding Information:Acknowledgments. We are grateful to L. M. C. Janssen for introducing us to the Gardner phase and to P. A. Zegeling for giving us insight into fractional calculus. We also thank J. de Graaf, S. Franz, M. Katsnelson, W. van Saarloos, J. Wettlaufer, T. H. Hansson, E. Barkai, B. Buča, and F. Wilczek for fruitful discussions. This work was supported by the Netherlands Organization for Scientific Research (NWO, Grant No. 680.92.18.05, C.M.S. and R.C.V.) and by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES, Finance Codes No. 001 and 0112, R.F.O.).
Publisher Copyright:
© 2021 American Physical Society.