Skip to main content
Log in

On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order

JETP Letters Aims and scope

Cite this article


The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time translation symmetry is observable only if the charge Q is not strictly conserved and may decay. This dichotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time τ Q of the charge Q and the energy relaxation time τ E . If τ Q ≫ τ E , the perturbed system relaxes first to the state with the ODLRO, which persists for a long time and finally relaxes to the full equilibrium static state. In the limit τQ → ∞, but not in the strict limit case when the charge Q is conserved, the intermediate ODLRO state can be considered as the ground state of the system at fixed Q with the observable spontaneously broken time translation symmetry. Examples of systems with quasi-ODLRO are provided by superfluid phase of liquid 4He, Bose-Einstein condensation of magnons (phase coherent spin precession) and precessing vortices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions


  1. F. Wilczek, arXiv:1308.5949.

  2. P. Bruno, Phys. Rev. Lett. 110, 118901 (2013).

    Article  ADS  Google Scholar 

  3. P. Bruno, Phys. Rev. Lett. 111, 070402 (2013).

    Article  ADS  Google Scholar 

  4. Ph. Nozieres, arXiv:1306.6229.

  5. Yu. M. Bunkov and G. E. Volovik, in Novel Superfluids, Ed. by K. H. Bennemann and J. B. Ketterson, International Series of Monographs on Physics, No. 156 (2013), Vol. 1, Ch. 4, p. 253; arXiv:1003.4889.

    Article  Google Scholar 

  6. S. Autti, Yu. M. Bunkov, V. B. Eltsov, et al., Phys. Rev. Lett. 108, 145303 (2012).

    Article  ADS  Google Scholar 

  7. R. A. Webb, R. L. Kleinberg, and J. G. Wheatley, Phys. Lett. A 48, 421 (1974).

    Article  ADS  Google Scholar 

  8. A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975).

    Article  ADS  Google Scholar 

  9. F. R. Klinkhamer, arXiv:1202.0531.

  10. R. J. Zieve, Yu. Mukharsky, J. D. Close, et al., Phys. Rev. Lett. 68, 1327 (1992).

    Article  ADS  Google Scholar 

  11. R. E. Packard, Rev. Mod. Phys. 70, 641 (1998).

    Article  ADS  Google Scholar 

  12. T. Sh. Misirpashaev and G. E. Volovik, JETP Lett. 56, 41 (1992).

    ADS  Google Scholar 

  13. J. J. Hosio, V. B. Eltsov, R. de Graaf, et al., Phys. Rev. Lett. 107, 135302 (2011).

    Article  ADS  Google Scholar 

  14. M. S. Foster, V. Gurarie, M. Dzero, and E. A. Yuzbashyan, arXiv:1307.2256.

  15. R. Matsunaga, Y. I. Hamada, K. Makise, et al., Phys. Rev. Lett. 111, 057002 (2013).

    Article  ADS  Google Scholar 

  16. A. A. Starobinsky, Phys. Lett. B 91, 99 (1980).

    Article  ADS  Google Scholar 

  17. F. R. Klinkhamer and G. E. Volovik, Phys. Rev. D 78, 063528 (2008); Phys. Rev. D 80, 083001 (2009).

    Article  ADS  Google Scholar 

  18. I. Bars, P. J. Steinhardt, and N. Turok, arXiv:1307.8106.

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to G. E. Volovik.

Additional information

The article is published in the original.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Volovik, G.E. On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order. Jetp Lett. 98, 491–495 (2013).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: