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arXiv · 1309.1845

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

G. E. Volovik
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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 reversal symmetry is observable only if the charge Q is not strictly conserved and may decay. This dihotomy 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 τ_Q and finally relaxes to the full equilibrium static state. In the limit τ_Q -> \infty, 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 reversal 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.

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G. E. Volovik. 2013-09-16. On the broken time translation symmetry in macroscopic systems: precessing states and off-diagonal long-range order. https://doi.org/10.1134/s0021364013210133

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