JETP Letters

, Volume 98, Issue 8, pp 491–495 | Cite as

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

  • G. E. VolovikEmail author


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.


Vortex JETP Letter Free Induction Decay Signal Energy Relaxation Time Trap Vortex 
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Copyright information

© Pleiades Publishing, Inc. 2013

Authors and Affiliations

  1. 1.Low Temperature Laboratory, Aalto UniversitySchool of Science and TechnologyHelsinkiFinland
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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