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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. Volovik
Article

Abstract

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.

Keywords

Vortex JETP Letter Free Induction Decay Signal Energy Relaxation Time Trap Vortex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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