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Abstract
We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spinsuperfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed outofequilibrium Bose–Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid 3He, experimentally observed in uniaxial aerogel 3Hesamples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a MinkowskitoEuclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar “ghost” condensate.
Original language  English 

Pages (fromto)  234–241 
Number of pages  8 
Journal  JETP Letters 
Volume  106 
Issue number  4 
DOIs  
Publication status  Published  14 Aug 2017 
MoE publication type  A1 Journal articlerefereed 
Keywords
 magnon BEC
 effective metric
 Polar 3He
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TOPVAC: From Topological Matter to Relativistic Quantum Vacuum
Volovik, G., Nissinen, J., Eltsov, V., Zhang, K., Rysti, J., Volard, M., Rantanen, R. & Mäkinen, J.
01/10/2016 → 30/09/2022
Project: EU: ERC grants

Centre of Excellence in Low Temperature Quantum Phenomena and Devices
Hietala, N., Mäkinen, J., Eltsov, V., Volovik, G. & Rysti, J.
01/01/2015 → 31/12/2017
Project: Academy of Finland: Other research funding