
VOLUME 98  ISSUE 8 
PAGE 549

On the broken time translation symmetry in macroscopic systems: precessing states and offdiagonal longrange order
G. E. Volovik
Low Temperature Laboratory, Aalto University, School of Science and Technology, P.O. Box 15100, FI00076 AALTO, Finland Landau Institute for Theoretical Physics of the RAS, 119334 Moscow, Russia
Abstract
The broken symmetry state with offdiagonal longrange order (ODLRO), which is
characterized by the vacuum expectation value of the operator of creation of the
conserved quantum number Q, has the timedependent 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 dihotomy is resolved in systems
with quasiODLRO.
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 , 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 ,
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 quasiODLRO are provided by superfluid phase of liquid
^{4}He, BoseEinstein condensation of magnons (phase coherent spin precession) and
precessing vortices.

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